The five-time NBA champion sustained the injury during the Lakers' 105-91 win at the Memphis Grizzlies on Tuesday, but is not expected to require surgery.
"Lakers guard Kobe Bryant, who hyperextended his left knee in Tuesday night's game at Memphis, had an MRI exam this morning and was examined by team physician Dr Steve Lombardo of the Kerlan Jobe Orthopaedic Clinic," a statement on the Lakers' official website read.
"Results of the MRI show that Bryant has a fracture of the lateral tibial plateau of his knee. He is expected to be out approximately six weeks."
Bryant only returned after six months out with an Achilles injury earlier this month. The 35-year-old had played six games, averaging 13.8 points, before this latest problem.
The Team USA guard signed a new two-year contract extension last month.