Bryant suffered the injury Tuesday night during the visiting Lakers' 96-92 victory over the Memphis Grizzlies. The Lakers said Thursday that an MRI showed the fracture.
"All I can do is do the work. And do everything I can to be back at the highest level," Bryant told ESPN.
Bryant also took to Twitter after news of the setback was announced Thursday.
Bryant will not require any surgical procedures on the knee, according to a source. It's just a matter of letting the bone heal.
The injury is an undeniable blow to the Lakers, who in late November signed Bryant to a two-year, $48.5 million contract extension before the 35-year-old had made it back onto the court from a torn Achilles tendon he suffered in April.
"That's too bad," coach Mike D'Antoni said at the team's practice Thursday. "You hate it for Kobe. He worked so hard to get back. 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."
The injury news for the Lakers didn't get any better regarding Steve Nash.
The team also announced Thursday that the veteran point guard -- limited to just six games this season -- will miss an additional four weeks because of nerve root irritation.
Nash was re-evaluated during the team's just-completed road trip.
The Lakers moved fast to shore up their depleted backcourt, agreeing to a deal with Kendall Marshall on Thursday night. Marshall, who was taken 13th overall by the Phoenix Suns in the 2012 draft, had been playing with the Delaware 87ers of the D-League since being acquired off waivers earlier this month.
The deal with Marshall, a former star at North Carolina, was earlier reported by Yahoo! Sports and ESPN.
Bryant, meanwhile, entered the 2013-14 campaign hoping to become the first player to rupture an Achilles and make it all the way back to All-Star status since Dominique Wilkins in 1992-93.
He returned to the court Dec. 8 -- in L.A.'s 20th game of the season -- and was averaging 13.8 points and 6.3 assists in six games, shooting 42.5 percent from the field and averaging 29.5 minutes. He tied his season high with 21 points on 9-of-18 shooting in Tuesday's win against the Grizzlies, hitting a deep 3-pointer late in the fourth quarter to help seal the win.
Prior to that big shot, Bryant went to the floor with 3:25 left in the third quarter. He stayed down briefly before standing up, and Bryant bent over at the waist as he flexed his left leg back and forth. He walked to the bench with trainer Gary Vitti but returned to the court following the timeout.
Bryant said after the game, in which he played a season-high 33 minutes, that he twisted his knee but it felt all right.
"I just hyperextended it," Bryant said. "I tend to hyperextend my knees every now and then."
D'Antoni said Thursday that he didn't think Bryant came back too soon from the Achilles injury.