The injury, which happened during Tuesday's game against the Memphis Grizzlies, is a fracture of the lateral tibial plateau in his left knee, according to a Lakers tweet. An MRI exam determined that Bryant played an entire half with a fracture in his knee, ESPN reported.
Bryant finished the game with 21 points, helping the Lakers close out a four-game road trip with a 96-92 victory. It was Bryant's sixth game of the season.
"You hate it for Kobe. He's worked so hard to get back," said Lakers head coach Mike D'Antoni. "But he'll be back. He'll be back in six weeks, and we'll deal with it and weather the storm until he gets back."
In November, the Lakers signed the 35-year-old Bryant to a two-year, $48.5 million contract extension before he was back on the court from a torn left Achilles' tendon. He returned to the court Dec. 8.
Jordan Farmar is also out with an injury to his hamstring. Lakers say Xavier Henry will take over point guard duties.
The Associated Press contributed to this report.