Bucks general manager John Hammond made the announcement on Friday through the club's Twitter account.
"This morning in Milwaukee, Andrew had additional diagnostic tests performed on his left ankle. The results of the testing confirmed a left ankle fracture which will keep Bogut sidelined for a period of 8-to-12 weeks."
Bogut left Wednesday's game with what was originally called a left ankle sprain and did not return. He suffered the injury early on against the Rockets while battling for a rebound.
The Aussie native is averaging 11.3 points per game and 8.3 rebounds in just 12 games so far this year. He missed four games earlier this season due to personal reasons, and missed one other contest due to a concussion.
For his career, the former first-overall pick of the Bucks in 2005, Bogut averages 12.7 points per game to go along with 9.3 rebounds and 2.3 assists.