Konerko sustained the injury making a tag in Chicago's game Tuesday against the Minnesota Twins.
The injury isn't season-ending, but Konerko could miss up to a week. According to MLB.com's Scott Merkin, Konerko has been told he can't further damage his hand by playing through the injury.
The 38-year-old announced earlier this year that he will retire after this season. The 18-year-veteran has hit .279 with an .842 OPS and 439 home runs over his career and has made six All-Star teams.
This season, Konerko is hitting .220 with five home runs in 186 at-bats.
- Ben Estes