The Pirates recalled infielder Vinny Capra from Triple-A Indianapolis in a corresponding move. Capra got into Pittsburgh's 11-1 win over the St. Louis Cardinals on Monday night, and had a pinch-hit single in the eighth.
Davis, 23, was the Pirates' first overall choice in the 2021 amateur draft and made his major league debut on June 19 of this season. Davis has primarily played right field and made two appearances so far at catcher.
It was unclear when Davis injured the hand. He played in Pittsburgh's 2-0 loss to the Minnesota Twins on Sunday, going 0-for-3 at the plate.
In 51 games thus far, Davis has batted .213 with five home runs, eight doubles and 18 RBIs.
Capra, 27, made his MLB debut last season for the Toronto Blue Jays and played eight games for them. He appeared in two big-league games earlier this year for Pittsburgh and went 0-for-4 with a walk and a run.
Information from Reuters contributed to this report.