Abreu, 27, has hit .260/.312/.595 (145 OPS+) with 15 home runs in 44 games this year. He signed a six-year, $68 million contract with the ChiSox over the winter. Abreu was leading the majors in homers at the time of his injury.
To make room on the roster, the White Sox optioned infielder Marcus Semien to Triple-A. He hit .218/.287/.327 (70 OPS+) with three homers and three steals in 43 games this season.
Chicago opens a three-game series with the Dodgers on Monday. Abreu and fellow Cuban star Yasiel Puig will meet head-to-head for the first time.