Bynum underwent an MRI on Sunday, but spokesman John Black said the team wouldn't have the results until the next day.
"Everybody's just upset for him and disappointed for him," Bryant said before practice Sunday as the Lakers prepared to play at the Knicks on Monday night. "But hopefully everything will be OK. We're all optimistic about it."
The 7-foot, 285-pound Bynum's injury brought back bad memories of last season for the Lakers. He went down in mid-January and was expected to be sidelined 8 to 12 weeks after bruising a bone in his knee and briefly dislocating his kneecap.
Instead, he missed the final 46 games of the season, as the Lakers lost in the NBA Finals. He underwent arthroscopic surgery May 21 to remove some cartilage debris and smooth some rough spots on the underside of his kneecap.
Bynum is the Lakers' third-leading scorer and second-leading rebounder this season, averaging 14.0 points, 8.2 rebounds and 1.9 blocks.
But the injury came as the 21-year-old seemed to be taking a major step forward in his fourth NBA season. In the five games before he was hurt, he was averaging 26.2 points, 13.8 rebounds and 3.2 blocks and shooting 65.3 percent from the field.