Red Sox manager Alex Cora said postgame that Betts will get treatment Monday and is expected to play Tuesday afternoon when the Red Sox open a three-game series with the New York Yankees in the Bronx.
Cora said the move to take out Betts was precautionary. The three-time All-Star leads the majors with a .337 batting average and is a contender for MVP.
In June, Betts hit the disabled list with left side soreness and missed 12 games. Cora said the latest injury was not related to that.
"I'll be ready to go Tuesday," Betts said, adding that the side doesn't hurt when he bats, but that when he throws it's a little sore.
Betts caught a fly ball from Jeff McNeil in the sixth inning and threw home as Austin Jackson held at third. Wilmer Flores followed with another drive to right, and Betts unsuccessfully threw home as Jackson scored on the sacrifice fly.
Betts went down to one knee, and was stretching his left side and back as a team athletic trainer and Cora jogged to the outfield. Betts walked off slowly and was replaced by Tzu-Wei Lin, who went into center. Jackie Bradley Jr. moved to right.
The win over the Mets cut Boston's magic number to two for a third straight AL East title.
Cora also said that infielder Eduardo Nunez (right knee soreness) likely will be back in the starting lineup Tuesday.
The Associated Press contributed to this article.