After undergoing a series of tests this week, General Manager John Hammond said Wednesday the 7-foot Australian suffers from an incomplete stress fracture in his lower back.
The plan is for rehab with rest and strengthening exercises, and have him re-evaluated once the recovery time has been reached.
Bogut recently sat out an eight-game stretch, but returned to play 16 minutes each game in victories over Toronto last Friday and Atlanta Saturday.
"Obviously, it doesn't make me feel good and I've been trying to do a little more weights and get a different strategy to get ready," Bogut, 24, told the Milwaukee Journal-Sentinel Monday.
In 36 contests this season, Bogut has averaged 11.7 points and 10.3 rebounds, making him one of just 13 NBA players with double-double per-game averages this season.