The White Sox placed Eaton on the 10-day injured list Thursday (retroactive to Tuesday) because of a strained right hamstring. They recalled right-handed reliever Zack Burdi from Triple-A to take Eaton's spot on the 26-man roster.
Eaton hasn't played since Monday's 5-2 loss to the Tampa Bay Rays.
The White Sox signed Eaton to a one-year contract in December. He played for the organization from 2014 to 2016.
Eaton likely hoped for a rebound season in 2021 after he hit .226/.285/.384 with four homers and 17 RBI in 41 games with the Washington Nationals last year. However, he's only put up a .641 OPS in 54 appearances.
The White Sox seemed to have one of the deepest outfields in MLB coming into the season, but Eaton joins Eloy Jimenez and Luis Robert on the injured list. Leury Garcia, Jake Lamb, Andrew Vaughn and Adam Engel will carry the load until Eaton can return.