The White Sox said it was a non-displaced fracture with no surgery required.
Benintendi was plunked on his hand by a fastball from Cleveland right-hander Logan Allen in the first inning. He was checked out by a trainer and then removed from the game.
Benintendi is unlikely to be ready for Opening Day. The White Sox open against the Los Angeles Angels on March 27 in Chicago.
Benintendi, 30, has a .270 career batting average with 98 homers, 493 RBIs and 85 steals in 1,031 games over nine seasons with the Boston Red Sox (2016-20), Kansas City Royals (2021-22), New York Yankees (2022) and White Sox.
He was an All-Star in 2022 with the Royals before being traded to the Yankees two weeks later. In two seasons with the White Sox, Benintendi has posted a .246/.309/.374 slash line with 25 homers and 16 steals. He cracked 20 homers last year to tie the career high he set in 2017 with the Red Sox.