It was his second straight missed game due to the injury.
Alonso, who had an MRI exam before Thursday's game, told reporters that he may sit out Friday's game against the Red Sox.
"I don't think it's anything serious," Alonso said before the game. "I'm hoping we give it a few days and I'll be ready."
With 12 home runs and 29 RBIs, he leads the A's in both categories.
"I want to be out there," he said. "It just sucks. But I understand my body, so I'm trying to be cautious and make sure this is two days and not two months."