Burstyn was born in New York City, the son of the late Yiddish-language actors, Pesach Burstyn and Lillian Lux. He is no relation to Ellen Burstyn (who was born Edna Rae Gilooley). Burstyn started performing on stage at Yiddish theaters from childhood, in musicals and melodramas produced by his father Pesach Burstein, especially as part of the Four Bursteins (he and his twin sister were billed as Motele and Zisele), in standard Pesach Burstein productions like A Khasene in Shtetl (A Wedding in the Village). He headed out on his own after reaching adulthood, in a bid to reach audiences bigger than the Yiddish stage.
He has been on American television, Broadway, Israeli theater, Dutch Television, The Mike Burstyn Show (1978-1981) and Yiddish theater. Notably, he was cast as lead in Israel Becker’s Shnei Kuni Leml (The Flying Matchmaker, an Israeli film).
Among his most noted roles in Yiddish theater was the part in his father’s production of Itzik Manger’s Songs of the Megillah (Yiddish: Megille Lider – the longest running Yiddish production to date in Israel, released on Broadway as Megilla of Itzik Manger).
Burstyn appeared on Broadway in, among other shows, Barnum, where he replaced British actor Jim Dale in the title role. He was nominated for Drama Desk Awards for his performance as Mayer in The Rothschilds off-Broadway in 1990 and in On Second Avenue in 2005.
Burstyn holds dual Israeli-American citizenship. He is also a performer, actor and singer in Israel.
The documentary The Komediant documents the lives and careers of the musical Burstyn family.
In the 2009, theatrical adaption by Joseph Bologna “Lansky” is portrayed by Mike Burstyn in a one act play.