The Angels said they would have an update on Simmons following the surgery. He will be placed on the disabled list.
Simmons, 26, was hurt when he landed awkwardly on his glove hand while diving to stop a grounder hit by Evan Longoria in the third inning of Sunday's 3-1 loss to the Tampa Bay Rays. He immediately left the game.
Simmons is one of the majors' best fielders. He won two Gold Glove awards with the Braves before they traded him to Los Angeles in the offseason. He has been a strong fielder in his first season with the Angels, though he made a throwing error in a loss Saturday.
Simmons has struggled at the plate this season, batting .219 with eight RBIs. He had a hit Saturday to end an 0-for-21 skid.
The Angels entered Monday fourth in the AL West at 13-18.
Information from The Associated Press was used in this report.