The injury is the latest setback in a disastrous season for the 26-year-old Gray, who already has been on the DL because of a right shoulder injury.
Gray, a 2015 All-Star who last season finished third in AL Cy Young balloting, had the highest ERA in the majors (5.84) going into Saturday.
"He had really good stuff today, so it's unfortunate to hear that he's hurt because this is the best he's looked in a long time," A's catcher Stephen Vogt said Saturday.
Gray (5-11) first felt the injury after striking out Dexter Fowler with a curveball in the top of the fourth.
"I was trying to go back out there for the sixth," Gray said after the game. "I told them after the fourth I had a little bit of an issue come up, and when I went back out for the fifth, it kind of felt the same.
"They kind of decided to shut it down there. I lobbied to go back out there. It obviously wasn't going to happen."
Information from The Associated Press was used in this report.