After graduating from Green Bay East High School, site of Packers home games until 1957, Smith moved on to the University of Notre Dame. After graduation, he worked for the Milwaukee Sentinel, St. Louis Journal, and Philadelphia Record.

After 18 years, Smith joined the New York Herald Tribune. He cemented his reputation with the Herald-Trib, as his column was widely read and often syndicated. When the paper folded in 1966, he became a freelance writer. He joined the New York Times in 1971 as a contract writer. By this time, his reputation was secured as one of the foremost sportswriters in America.

During his time with the Times, Smith garnered many awards. In 1976, he was the first sportswriter to win the Pulitzer Prize for Commentary. He also received the J. G. Taylor Spink Award from the Baseball Hall of Fame in 1976. Furthermore, the Associated Press awarded him the first Red Smith Award for "outstanding contributions to sports journalism."

Smith was a strong critic of former world heavyweight boxing champion Muhammad Ali throughout Ali's career. When Ali refused to serve during the Vietnam War, claiming his case as a conscientious objector, Smith rounded on him. Despite not serving in any army during his own lifetime the reporter noted, "Squealing over the possibility that the military may call him up, Cassius makes himself as sorry a spectacle as those unwashed punks who picket and demonstrate against the war", and berated Ali for being a "draft dodger" and a "slacker".

Later Smith famously commented on Ali's first professional defeat in 32 bouts against Joe Frazier: "If they fought a dozen times, Joe Frazier would whip Muhammad Ali a dozen times; and it would get easier as it went along". Ali went on to fight Frazier twice more, winning both times, once by unanimous decision and once by TKO.

Smith died at the age 76 of heart failure. Red Smith Middle School in Green Bay is named in his honor. Also named in his honor is the Red Smith Handicap, a race for Thoroughbred horses run at Belmont Park on Long Island, New York.

Red's son, Terence Smith, went on to be a journalist at The New York Times, CBS News, PBS, and NPR.

Smith is buried in Stamford's Long Ridge Union Cemetery.