General manager John Hammond said late Thursday that Bogut suffered a leg strain and contusion in Wednesday's 99-85 victory over New Jersey.
The Aussie scored 21 points and 11 rebounds before leaving the game in late in the fourth quarter.
An MRI revealed the injury on Thursday.
Bogut, 24 and in his fifth NBA season, is averaging 16.1 points and 9.2 rebounds per game. The Bucks hope to get shooting guard Michael Redd back in the starting lineup soon.