Coleman gave up six runs, three hits and three walks in one-third of an inning Monday against San Francisco. He has had the injury since early in spring training.
Coleman and second baseman Omar Infante, who has a bone spur in his right elbow, were to be left in Surprise when the Brewers head to Milwaukee later Wednesday for a pair of exhibition games.
''Louie is a big, big part of our bullpen when healthy,'' manager Ned Yost said Wednesday. ''Omar is a big part of our infield defense and our offensive lineup. We have to have a guy that can play second base if he can't start out the season.''
Infante hit .318 in 118 games last season with Detroit and agreed to a $30.25 million, four-year contract with the Royals. Pedro Ciriaco, who played with Kansas City, Boston and San Diego last year, could open at second base if Infante is not ready.
Coleman was 3-0 with a 0.61 ERA in 23 relief appearances last year.
Infante was to play second Wednesday and be a designated hitter the following day, both in minor league exhibitions
''I think Omar is going to be OK,'' Coleman said. That's just my gut feeling.''
Yost said the Royals may open with a six-man bullpen.