Several episodes of The Nanny reference when Fran was in the production of Fiddler or use the lines of the song, such as the lyrics from Matchmaker, in their script.
A segment on Sesame Street parodies "If I Were a Rich Man" themed around the letter B.
Another, part of the Monsterpiece Theatre series of segments, uses a parody of "Tradition" called "Addition", about adding extra fiddlers to the roof of a house. The roof ends up caving in from the weight of all those fiddlers.
In the Broad City episode "Friendiversary," Ilana tells Abbi that her great-grandmother came to America during Fiddler on the Roof times.