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.
Animaniacs: Parodied in the Goodfeathers segment "Pigeon on the Roof", because who better to parody a Jewish musical than a cast of Italian-American pigeons?
The Lion King 1½: After Simba beats Timon in a slug-slurping contest, Timon and Pumbaa proceed to sing "Sunrise, Sunset".