The Warriors have called the injury a sprain and were delaying further testing to let the injury "calm down," according to the team.
The MRI was originally set for Monday night but was later pushed to Tuesday.
That leaves Bogut's status in question as the series heads back to Cleveland for Game 6 on Thursday. The Warriors lead the series 3-2.
"It would have been nice to have him available, but we played four, five different people at center, just trying to find something that would work," Warriors coach Steve Kerr said, according to the San Francisco Chronicle.
"It's unfortunate. Hopefully he's OK. We need him."
The injury happened when Bogut collided with Cleveland Cavaliers guard J.R. Smith as they positioned themselves for a rebound. Smith fell into Bogut's leg, which hyperextended backward as he fell to the court. Bogut writhed in pain, and he stayed on the baseline until play was halted.
He was unable to leave the floor under his own power, limping as he was helped to the locker room and grasping his jersey in his mouth as he tried to deal with the pain.
The Warriors already were thin because forward/center Draymond Green was suspended for Game 5.
Bogut started but played just eight minutes and contributed three rebounds and three blocks Monday night. He is averaging 4.6 points, 5.7 rebounds and 1.6 blocks in 16.6 minutes per game this postseason.
Bogut collides with Smith, left knee buckles
J.R. Smith drives to the basket and Andrew Bogut goes up to block the shot. Bogut collides with Smith, then lands awkwardly, causing his left knee to hyperextend.