Albats' father, Mark Yevgenyevich Albats, was a member of a GRU military reconnaissance team during World War II, residing in German-occupied Ukraine. In 1943 he was wounded and discharged from the Army. Afterward he worked as an engineer at a scientific institution, designing radiolocation systems for the Soviet Army. Albats' mother, Yelena Izmaylovskaya, was an actress and a radio news host. Albats' elder sister, Tatyana Komarova, is a television host/anchor.

Yevgenia Albats graduated from the Department of Journalism of Moscow State University in 1980. One of her classmates and friends was Anna Politkovskaya, who would become an investigative journalist and was assassinated in 2006.

Albats was married to journalist, writer and science popularizer Yaroslav Golovanov.

Albats started her professional work as a science observer writing about astrophysics and particle physics for the Izvestia newspaper's Sunday supplement,Nedelya. From 1986 - 1992 she worked for the Moscow News. In 1996-2006 she worked for Izvestia (led the weekly column We and Our Children) and Novaya Gazeta.

She received the Golden Pen Award from the Russian Union of Journalists