Beltre, who had two hits and two RBIs against the Boston Red Sox, suffered the injury sliding into second base in the fifth inning.
X-rays were negative, and team physician Dr. Keith Meister diagnosed a sprain after examining Beltre. The third baseman, who was being fitted for a splint, also needed four stitches for a cut he sustained on the play.
Utility infielder Adam Rosales replaced Beltre in the lineup.
The Rangers are off Monday before beginning a three-game series against the Chicago White Sox on Tuesday.
Beltre, who had singled in the inning, slid into second trying to break up a double play. After being called out, Beltre stayed on all fours for about a minute while grabbing his thumb.
He is hitting .257 with six homers and 18 RBIs this season.
The Associated Press contributed to this report.