Baryshnikov (whose name is sometimes transliterated as Baryshinikov or Barishinikov) was born in Riga, Soviet Union (now Latvia) to Russian parents. His father was an engineer and his mother a seamstress.

He first entered the Vaganova Ballet Academy in 1960. Due to his talent, he joined Leningrad's Kirov Ballet in 1966. While touring Canada with the Bolshoi Ballet in 1974, Baryshnikov disappeared for several days, reappearing in the United States, where he applied for political asylum.

From 1974 to 1979, he was principal dancer with the American Ballet Theatre (ABT), though he also danced with ballet and modern dance companies around the world. He then joined the New York City Ballet for fifteen months, working with choreographer George Balanchine. He returned to ABT in 1980 as dancer and artistic director, a position he held for a decade. On July 3, 1986, he became a naturalized citizen of the United States. From 1990 to 2002, Baryshnikov was artistic director of the White Oak Dance Project, a touring company he co-founded with Mark Morris.

Baryshnikov was a unique dancer in many ways. He was short and thus never danced in ballets like Swan Lake where a taller, more noble bearing was expected. His dancing was renowned for its textbook form, technical brilliance, and emotional detachment.

He was a recipient of Kennedy Center Honors in 2000. As of 2004, he is actively involved in the establishment of the Baryshnikov Arts Center in a new performing arts complex in New York City.

He has a daughter, Alexandra Baryshnikov, with actress Jessica Lange and three younger children (Sofia, Anna, and Peter) with former ballerina Lisa Rinehart.