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.
Crawford, 25, allowed five earned runs in two innings Sunday, taking the loss in his major league debut as the Red Sox fell 11-5 to the Indians.
"He filled up the strike zone with good stuff," Red Sox manager Alex Cora said. "It's not easy to come into a situation like this and maneuver a big league lineup."
Crawford found out after Saturday's minor league game that he'd be starting in the majors.
"It's kind of been a crazy 24 hours," he said. "I was kind of uncertain what the plan was with all the COVID stuff. I was told to kind of be on standby. After the game I was told I was starting today. I tried to get as much sleep as possible. Obviously, I was super excited. ... Unfortunately, it didn't go as I wanted it to, but we live and we learn and we're going to make adjustments and move forward."
Pivetta, 28, is 9-7 with a 4.67 ERA in 26 starts.
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 remain 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 and also lost Sunday. Boston has a three-game lead over Seattle for the second wild card.
The Associated Press contributed to this report.