Jimenez, who suffered the injury while running from first to third during Monday's game, is expected to be sidelined for two to three weeks. He is batting .211 (4-for-19) with two doubles, three RBIs and six strikeouts through five games this season.
"He worked hard this offseason. He's in great shape. It's just one of those things that happens," White Sox manager Pedro Grifol said. "The good thing is he came in today and felt strong. We're extremely optimistic he'll be available to us in the near future."
He was limited to 84 games last season after appearing in only 55 games in both 2020 and 2021.
In a related roster move, the White Sox recalled infielder Jake Burger from Triple-A Charlotte.
Burger batted .250 with eight homers and 26 RBIs in 51 games with the White Sox last season. He is hitting .167 (2-for-12) with a double through three games with Charlotte in 2023.
ESPN's Jesse Rogers and Reuters contributed to this report.