Pomeranz was injured when he whacked the back of a chair Monday night following his shortest outing of the season. Right-hander Evan Scribner, who was on Oakland's opening-day roster, was recalled from Triple-A Sacramento.
The A's also acquired minor league lefty Brad Mills from the Milwaukee Brewers for cash.
Pomeranz took the loss Monday night against Texas after allowing a career-high eight runs — seven earned — in 3 2-3 innings. He was called into manager Bob Melvin's office before addressing the media after the game.
Pomeranz, who was holding a plate of food in his right hand, did not indicate anything was wrong when speaking to reporters.
"I know it wasn't intentional, but at the same time he has to realize there are consequences," Melvin said. "I know it was out of frustration, but it is disappointing. It affects how we go about our business here. He was throwing well for us."
Pomeranz is 5-4 with a 2.91 ERA in 17 games, including eight starts, with the A's.
He began the season in the bullpen, going 1-1 with a 1.98 ERA in nine relief appearances. He moved into the starting rotation May 7 and is 4-3 with a 3.21 ERA in eight starts since. This is his second career stint on the DL.
Mills has spent the entire season at Triple-A Nashville, where he was 4-2 with a 1.56 ERA in 14 games, including 12 starts. His ERA was the lowest in the Pacific Coast League.