An MRI exam on Thursday confirmed the injury, which Howard suffered 55 seconds into the first quarter of Wednesday night's loss to the Detroit Pistons. He did not return.
It will be the eighth game this season Howard has missed; he missed seven games for health issues and missed the season opener due to a league-mandated suspension stemming from the 2015 playoffs.
Howard is third in the NBA in rebounds at 12.1 per game, and over the last 17 games, he had averaged 16.6 points.
The Rockets are also dealing with other injury issues, with starting point guard Patrick Beverley (left ankle sprain), backup guard Jason Terry (right knee pain) and rookie power forward Montrezl Harrell (right shoulder contusion) listed as questionable for the Bucks game.
"We got to figure it out," guard James Harden said. "We've been through this situation before a lot last year. Guys are going to have opportunities to play extra minutes and just take advantage of it."