Choo went on the disabled list Tuesday for the fourth time this season. The fracture occurred during Monday's 5-2 win over Oakland on a pitch from left-hander Ross Detwiler and is likely to end the right fielder's season.
The surgery will be performed by Dallas hand specialist Dr. Thomas DiLiberti.
When catcher Robinson Chrinos had similar surgery in April, he missed 53 games over two months. The AL West-leading Rangers had 41 games left in the regular season after Tuesday night's game against the Athletics.
The Rangers recalled outfielder Ryan Rua from Triple-A Round Rock and he was in the lineup Tuesday against the Athletics in right field, Choo's regular position. Jurickson Profar was the leadoff hitter, playing left.
Choo first went on the DL on April 9 and missed 35 games with a strained right calf, then returned for only one game before going back on the disabled list May 23 and missing 19 games with a strained left hamstring. Before getting hit by the pitch Monday, Choo had been back less than two weeks from a 15-day DL stay caused by lower back inflammation.