During the Prologue ("Tradition"), Tevye explains the role of God's law in providing balance in the villagers' lives. He describes the inner circle of the community and the larger circle, which includes the constable, the priest and countless other authority figures. He explains, "We don't bother them and so far, they don't bother us." He ends by insisting that, without their traditions, he and the other villagers would find their lives "as shaky as a fiddler on the roof."
Three of Tevye's daughters, Tzeitel, Hodel and Chava, wonder if the matchmaker will ever find them the men of their dreams ("Matchmaker"). The matchmaker, Yente, tells Golde that she has selected the butcher, Lazar Wolfe, as a match for Tzeitel.
Tevye reflects on how much he wishes he had a small fortune ("If I Were a Rich Man"). A group of villagers, including an outsider, Perchik, approaches him with news of a violent pogrom in a nearby village. Tevye invites Perchik, a young revolutionary student, to come to his home for Sabbath dinner and arranges for him to instruct his daughters.
Motel, the tailor, attempts to ask Tevye for Tzeitel's hand, but gets tongue-tied. The family and their guests welcome the Sabbath ("Sabbath Prayer").
Tevye goes to meet Lazar Wolfe, the butcher, and agrees to the match with Tzeitel. A boisterous celebration ensues, involving the villagers and the Russians, who also congregate in the tavern ("L'Chaim").
As Tevye staggers home, he meets the Constable, who warns him that a demonstration is going to be planned against the Jews of Anatevka. In his inebriation, Tevye conjures The Fiddler, who plays his violin as Tevye dances his way home.
Tevye appears and tells Tzeitel about her engagement to Lazar Wolfe. Golde rejoices but, after she leaves, Motel tells Tevye that he and Tzeitel gave each other a pledge to marry. After a struggle with himself, Tevye agrees to their marriage. He leaves and Motel and Tzeitel rejoice ("Miracle of Miracles").
Tevye decides to manufacture a wild nightmare ("The Dream") to convince Golde that the match with Lazar will result in Tzeitel's death at the hands of the butcher's first wife, Fruma-Sarah. Golde is so horrified that she insists on a marriage between Tzeitel and Motel.
The villagers are gossiping in the street about the mix-up in Tzeitel's wedding plans. As Chava enters Motel's tailor shop, a group of Russians on the street taunt her. Fyedka, a Russian youth, insists that they stop. After they leave, Fyedka follows Chava into the shop. He tries to speak with her, but leaves quickly when Motel enters. Motel places his wedding hat on his head.
The musicians lead us to the wedding. The company sings ("Sunrise, Sunset") as the traditional Jewish ceremony takes place. To the villagers' dismay, Perchik asks Hodel to dance with him, and she accepts, performing the forbidden act of dancing with a man. Everyone else follows suit. As the dance reaches a wild high point, the Constable and his men enter. They destroy everything in sight. Perchik grapples with a Russian and is hit with a club. The constable bows to Tevye and says " I am genuinely sorry. You understand?" Tevye replies with mock courtesy, "Of course." The family begins to clean up after the destruction.