The ban includes post-season games, MLB said.
Baltimore, which owns a 10-game lead atop the American League East, has 17 regular-season games remaining.
Davis, a 28-year-old first baseman, is batting only .196 this season but has 26 home runs. He hit a big-league-leading 53 last year.
The Orioles are already without catcher Matt Wieters and third baseman Manny Machado, both of whom sustained season-ending injuries.