Eaton, 25, left Friday night's game in the fourth inning after going 0-2 with a walk. He is hitting .276 (27-for-98) with one home run, 14 RBIs and 20 runs scored over 25 games this season, his first with the White Sox. He is tied for seventh in the American League in runs scored.
The White Sox also recalled left-handed pitcher Frank De Los Santos from Triple-A Charlotte, claimed outfielder Moises Sierra off waivers from Toronto and transferred right-handed pitcher Nate Jones to the 60-day disabled list.
De Los Santos, 26, has made eight relief appearances this season between Charlotte and Double-A Birmingham, going 1-0 with a 0.63 ERA and 10 strikeouts. He was acquired from the Tampa Bay Rays on Sept. 13, 2013 in exchange for cash considerations and has no big league experience.
Sierra, 25, was designated for assignment by the Blue Jays on May 1 after going 2-for-34 (.059) with two RBIs and two runs scored in 34 games this season. He is a career .229 hitter (66-for-288) with seven home runs and 30 RBIs in 97 games over three seasons with Toronto (2012-14).
Jones, 28, has not pitched in a game this season after being placed on the disabled list on April 4.