While this has ended Bogut’s chances of competing in the rest of the NBA Finals, the centre has not completely ruled out his Olympic cause.
"I'm not great at math but six to eight weeks minimum is what I've been told," Bogut said.
"It's very unlikely at this point, to be honest.
"We are going to re-evaluate it in a month and if a miracle happens and it feels great in a month and I can get back on the court, we'll see."
The injury does not require surgery and Bogut is expected to make a full recovery.
“First and foremost, my heart goes out to Andrew,” said Boomers head coach Andrej Lemanis.
“I know how much he was looking forward to joining his Australian teammates and competing in the green and gold singlet in Rio.
“He has had a terrible run of luck with injuries during his career and I am truly disappointed for him.
“His contribution to the sport of basketball in this country has been enormous and he deserves to again have that Olympic experience.
“We will continue to work with and support Andrew during the rehab phase, providing whatever he needs to ensure his recovery is a complete success.
“The welfare of the player is always the most important consideration. I am thankful that the injury is not one that requires surgery and is predicted to have him out of the game for only a short period.
“Of course, if the recovery happens quicker than expected, then we will work with the circumstances in front of us and see what it means at that point in time.
“Dealing with injuries is a reality of any campaign. As a team, we have tremendous depth of talent and a wonderful spirit. We will continue to build and adapt as a group and I have great confidence that we will find a way to be successful.”
The NBA Finals continue today with the Warriors needing just one more win to clinch the title while Australian Matthew Dellavedova and the Cleveland Cavaliers look to force a Game 7 on Monday.