The Reds signed Baker to a minor-league contract Sunday and assigned him to Double-A Chattanooga.
Baker has been battling lat tightness and will pitch Friday against the Diamondbacks, Eric Stephen of TrueBlueLA.com reports.
Baker was claimed off waivers by the Brewers on Monday.
Baker, playing in his first season since Tommy John sidelined him in 2015, has allowed one run over five appearances for Double-A Akron.
Baker was optioned to Double-A Akron as part of the Tribe's first round of spring cuts.
Baker will compete for one of the few remaining bullpen spots in spring training, SB Nation reports.
Baker was optioned to Double-A Akron on Monday.