Bryant came down on the foot of Atlanta's Dahntay Jones after taking his final shot of the game, which turned out to be a miss with 4 seconds remaining and the Lakers trailing by two.
Bryant limped off the court under his own power, but the Lakers said after the game he had suffered a severely sprained left ankle and would be out indefinitely.
His absence could badly damage the Lakers' bid to earn a playoff spot after struggling for much of the season. They finished the night in eighth place in the Western Conference, holding a half-game lead over Utah for the final post-season berth.
Bryant hit a 3-pointer with 18 seconds left to bring the Lakers within one, but he missed three other shots during the closing 90 seconds -- the last one doing the damage to his ankle.
After Bryant gave the Lakers a chance with his 3-pointer, Korver hit 1-of-2 from the foul line. Following the last miss by Bryant, Korver grabbed the rebound and then hit two free throws with 2.6 seconds remaining to clinch the victory. Atlanta ended a three-game losing streak.
Devin Harris led Atlanta with 17 points and Korver had 15. Bryant had 33 points, but went 11-of-33 from the field while the Lakers were shooting 39 percent as a team.
Los Angeles is in the midst of a stretch in which it will play 8-of-10 on the road.
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