Born in Riga in Livonia, then part of the Russian empire, the Jewish German-speaking Nimzowitsch came from a wealthy family, where he learned chess from his father, who was a merchant. In 1904, he traveled to Berlin to study philosophy, but set aside his studies soon and began a career as a professional chess player that same year. He won his first international tournament at Munich 1906. Then, he tied for first with Alexander Alekhine at St. Petersburg 1913/14 (the eighth All-Russian Masters' Tournament).

During the 1917 Russian Revolution, Nimzowitsch was in the Baltic war zone. He escaped being drafted into one of the armies by feigning madness, insisting that a fly was on his head. He then escaped to Berlin, and gave his first name as Arnold, possibly to avoid anti-Semitic persecution.

Nimzowitsch eventually moved to Copenhagen in 1922 (some sources say 1920), which coincided with his rise to the world chess elite, where he lived for the rest of his life in one small rented room. In Copenhagen, he won twice Nordic Chess Championship in 1924 and 1934. He obtained Danish citizenship and lived in Denmark, until his death in 1935. Although he had long suffered from heart trouble, his early death was unexpected, taken ill suddenly at the end of 1934, he lay bedridden for three months before dying of pneumonia. He is buried in Bispebjerg Cemetery in Copenhagen.

The height of Nimzowitsch's career was the late 1920s and early 1930s. Chessmetrics places him as the third best player in the world, behind Alexander Alekhine and Jose Capablanca, from 1927 to 1931. His most notable successes were first-place finishes at Copenhagen 1923, Marienbad 1925, Dresden 1926, Hannover 1926, and the Carlsbad 1929 chess tournament, and second place behind Alekhine at the San Remo 1930 chess tournament. Nimzowitsch never developed a knack for match play, though; his best match success was a draw with Alekhine, but the match was only two games long and was in 1914, thirteen years before Alekhine became world champion.

Nimzowitsch never won against Capablanca, but fared better against Alekhine. He even beat Alekhine with the black pieces, in their short 1914 match at St Petersburg. One of Nimzowitsch's most famous games is his celebrated immortal zugzwang game against Sämisch at Copenhagen 1923. Another game on this theme is his win over Paul Johner at Dresden 1926. When in form, Nimzowitsch was very dangerous with the black pieces, scoring many fine wins over top players.

Nimzowitsch is considered one of the most important players and writers in chess history. His works influenced numerous other players, including Savielly Tartakower, Milan Vidmar, Richard Réti, Akiba Rubinstein, Bent Larsen, and Tigran Petrosian, and his influence is still felt today.

He wrote three books on chess strategy: Mein System (My System), 1925, Die Praxis meines Systems (The Practice of My System), 1929, commonly known as Chess Praxis, and Die Blockade (The Blockade), 1925. The last of these has just been reissued in a volume containing both the German original and the English translation published by Hardinge Simpole. However, much that is in it is covered again in Mein System. It is said that 99 out of 100 chess masters have read Mein System; consequently, most consider it to be Nimzowitsch's greatest contribution to chess. It sets out Nimzowitsch's most important ideas, while his second most influential work, Chess Praxis, elaborates upon these ideas, adds a few new ones, and has immense value as a stimulating collection of Nimzowitsch's own games, even when these games are more entertaining than instructive.

Nimzowitsch's chess theories flew in the face of convention. While there were those like Alekhine, Emanuel Lasker, and even Capablanca who did not live by Tarrasch's rigid teachings, the acceptance of Tarrasch's ideas, all simplifications of the more profound work of Wilhelm Steinitz, was nearly universal. That the center had to be controlled by pawns and that development had to happen in support of this control ... the core ideas of Tarrasch's chess philosophy ... were things every beginner thought to be irrefutable laws of nature, like gravity.

Nimzowitsch shattered these assumptions. He discovered such concepts as overprotection (the least important of his ideas from a modern standpoint though still interesting and sometimes applicable), control of the center by pieces instead of pawns, blockade, and prophylaxis ... playing to prevent the opponent's plans. He was also a leading advocate and exponent of the fianchetto development of the bishops. Nimzowitsch also formalised strategies using open files, outposts and invasion of the seventh rank, all of which are widely accepted today. Others had utilized such ideas in previous years, but he was the first to knit them together into a cohesive whole.

Grandmaster (GM) Raymond Keene writes that Nimzowitsch "was one of the world's leading Grandmasters for a period extending over a quarter of a century, and for some of that time he was the obvious challenger for the world championship. ... [He was also] a great and profound chess thinker, second only to Steinitz, and his works-Die Blockade, My System and Chess Praxis-established his reputation as one of the father figures of modern chess." GM Robert Byrne called him "perhaps the most brilliant theoretician and teacher in the history of the game." GM Jan Hein Donner called Nimzowitsch "a man who was too much of an artist to be able to prove he was right and who was regarded as something of a madman in his time. He would be understood only long after his death."

Many chess openings and variations are named after Nimzowitsch, the most famous being the Nimzo-Indian Defence (1.d4 Nf6 2.c4 e6 3.Nc3 Bb4) and the less often played Nimzowitsch Defence (1.e4 Nc6). Nimzowitsch biographer Grandmaster Raymond Keene and others have referred to 1.f4 followed by 2.b3 as the Nimzowitsch-Larsen Attack. Keene wrote a book about the opening with that title. All of these openings exemplify Nimzowitsch's ideas about controlling the center with pieces instead of pawns. Nimzowitsch was also vital in the development of two important systems in the French Defence, the Winawer Variation (in some places called the Nimzowitsch Variation; its moves are 1. e4 e6 2. d4 d5 3. Nc3 Bb4) and the Advance Variation (1. e4 e6 2. d4 d5 3. e5). He also pioneered two provocative variations of the Sicilian Defence, both regarded as dubious today: the Nimzowitsch Variation, 1.e4 c5 2.Nf3 Nf6, which invites 3.e5 Nd5, similarly to Alekhine's Defence, and 1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 d5?!

There are many entertaining anecdotes regarding Nimzowitsch...some less savory than others. For example, he once missed the first prize of a great rapid transit tournament in Berlin by losing to Sämisch; immediately upon learning this, Nimzowitsch got up on a table and shouted "Gegen diesen Idioten muss ich verlieren!" ("That I should lose to this idiot!").

Nimzowitsch was annoyed by his opponents' smoking. A popular, but probably apocryphal, story is that once when an opponent laid a cigar on the table, he complained to the tournament arbiters, "he is threatening to smoke, and as an old player you must know that the threat is stronger than the execution".

Nimzowitsch had lengthy and somewhat bitter dogmatic conflicts with Tarrasch over whose ideas constituted 'proper' chess.

Nimzowitsch's vanity and faith in his ideas of overprotection provoked Hans Kmoch to write a parody about him in February 1928 in the Wiener Schachzeitung. This consisted of a mock game against the fictional player "Systemsson", supposedly played and annotated by Nimzowitsch himself. The annotations gleefully exaggerate the idea of overprotection, as well as asserting the true genius of the wondrous idea. Kmoch was in fact a great admirer of Nimzowitsch, and the subject of the parody himself was amused at the effort.

Kmoch also wrote an article about his nine years with Nimzowitsch:

Nimzovich suffered from the delusion that he was unappreciated and that the reason was malice. All it took to make him blossom, as I later learned, was a little praise. His paranoia was most evident when he dined in company. He always thought he was served much smaller portions than everyone else. He didn't care about the actual amount but only about the imagined affront. I once suggested that he and I order what the other actually wanted and, when the food was served, exchange plates. After we had done so, he shook his head in disbelief, still thinking that he had received the smaller portion.

Nimzovitsch's colleague Tartakower observed of him, "He pretends to be crazy in order to drive us all crazy."