The outfielder will return to Houston for further evaluation.
Alvarez, who was serving as the designated hitter, left Thursday's game against the Toronto Blue Jays after a ground out in the first inning. He said he first felt sore when hitting in the cage before the game and felt pain again when he swung and missed at the first two pitches in his lone at-bat.
"It's not easy to figure it out, but we'll make adjustments," manager Dusty Baker said before Friday's game vs. the Guardians. "You don't have a choice, you just have to go forward."
Alvarez is batting .272 with 17 home runs in 57 games.
Alvarez ranks second in the AL in homers and slugging percentage behind Aaron Judge of the Yankees. The Cuban National Series veteran was the AL Rookie of the Year in 2019 and made his first All-Star team last season, when he hit .306 with 37 homers and 97 RBIs.
Mauricio Dubon filled in for Alvarez in left field as Houston opened a three-game series at Cleveland.
The Associated Press contributed to this report.