The White Sox made the move with their leadoff man before Saturday night's game against Cleveland. Eaton was hurt running to first base while hitting into a double play Friday.
Eaton is batting .276 with 14 RBIs and two stolen bases. Chicago recalled left-hander Frank De Los Santos from Triple-A Charlotte and claimed outfielder Moises Sierra off waivers from Toronto.
Left-hander Chris Sale, on the DL since April 18 with a strained flexor muscle, played catch in the outfield. The two-time All-Star is expected to throw again Monday. Sale is 3-0 with a 2.30 ERA in four starts.
Right-hander Nate Jones will have back surgery Monday and was put on the 60-day DL. He got into two games last month, and manager Robin Ventura said Jones could return this season.