In addition, reserve Danny Santana also went on the list Sunday, meaning Boston has put 11 players on the list in about a week.
Pivetta was supposed to face Cleveland at 1 p.m. ET at Fenway Park. Instead, the Red Sox called up right-hander Kutter Crawford from Triple-A Worcester to take the start.
Pivetta, 28, is 9-7 with a 4.67 ERA in 26 starts. The 25-year-old Crawford is getting his first big league appearance.
Santana is batting .168 with four homers and 13 RBIs in 35 games. The Red Sox recalled outfielder Franchy Cordero to take his spot.
The Red Sox start the day in third place in the AL East, eight games behind the Rays. But they are only a half-game behind the Yankees, who own the first wild card. Boston has a four-game lead over Seattle for the second wild card.