Baker sprained his right thumb after an over-exuberant high five with a teammate that bent his thumb back to his wrist. The move to the disabled list is retroactive to June 13, the day he got hurt.
The Rangers announced the moves Tuesday before their game against Oakland.
Texas recalled rookie left-handed reliever Joseph Ortiz from the Triple-A Round Rock, along with catcher Robinson Chirinos.
McGuiness had started nine of the previous 11 games at first base, and had 13 strikeouts in 34 plate appearances.
Lance Berkman, after two days off, was in the lineup playing first base on Tuesday night.