Team officials declined to say how long Bryant would be sidelined until he could be reevaluated Friday in Los Angeles, though the injury has the potential to end his season.
The severity of the tear will determine Bryant's next course of action.
He probably needs season-ending surgery if it is a full tear, according to sports-medicine specialists, who were speaking in general terms about rotator cuff injuries.
If it is only a partial tear, Bryant might be able to return to action in a matter of weeks after rest and rehabilitation. Or Bryant, who has a notoriously high pain threshold, could try to play sooner than that and opt for surgery or rehabilitation later.
He was injured while dunking in the third quarter of a 96-80 loss to New Orleans on Wednesday.
"I felt fine when I went up, didn't feel too good when I came down," he said after the game, adding that the shoulder had bothered him for a while. He added that it "came out a little bit" but downplayed the pain, saying he had played with a torn labrum in his shoulder earlier in his career.
Bryant, 36, missed eight of the Lakers' last 16 games so he could rest.
He had 14 points against New Orleans and avoided using his right arm after returning in the fourth quarter. He took two left-handed shots, making a 14-foot turnaround but air-balling an eight-foot hook shot. He dribbled and passed almost exclusively with his left.
Some players didn't know he was injured.
"He was hurt?" New Orleans forward Anthony Davis said. "I just thought it was an awesome [left-handed] move, honestly. I thought he's been working on it."
But Bryant walked off the court and straight to the locker room after the Lakers called a timeout with 1:09 to play.
A full tear would mean surgery but "if it's a partial tear, he could return to play in two and six weeks depending on his response to treatment," said Keith Feder, a Manhattan Beach orthopedic surgeon who did not see Bryant's MRI results.
In a quirk of fate, Bryant was selected an All-Star starter for the 17th time Thursday, a few hours after the preliminary MRI test results were publicized.
Bryant, in his 19th season, received the second-most votes among Western Conference guards. Golden State's Stephen Curry led them with 1.5 million votes, followed by Bryant (1.15 million) and Houston's James Harden (1.07 million).
Whether Bryant plays in the Feb. 15 game is the great unknown.
If the Lakers (12-31) are looking for optimism, they can find it in the top-five protected draft pick they will almost surely keep if Bryant's season is done. They currently hold the NBA's fourth-worst record and are 2-6 without him this season.
Not that they have been that great with Bryant (10-25), whose scoring acumen has been tempered by poor shooting. He is averaging 22.3 points, 5.7 rebounds and 5.6 assists but shooting only 37.2%, more than eight percentage points below his career mark coming into this season.
Nick Young becomes the obvious benefactor if Bryant misses substantial time, though he has struggled badly this month, making only 31.5% of his shots in 11 games.
The torn rotator cuff could be the third major injury to hit Bryant the last two years. He was sidelined by a torn Achilles' tendon in April 2013 and sustained a broken bone in his knee after returning to action in December that year. All told, he played only six games last season.
Bryant is currently making $23.5 million and due a guaranteed $25 million next season.
He would be the fourth Lakers player to miss time with serious injuries this season. Rookie Julius Randle sustained a broken leg on opening night and Steve Nash declared himself done for the season after training camp because of recurring back problems. Xavier Henry was sidelined for the season in November because of a torn Achilles' tendon.
"There's been a lot of things that have gone wrong so I've just got to deal with it," Lakers Coach Byron Scott said. "It's like everybody else. Next guy up has got to be ready to play."
Follow Mike Bresnahan on Twitter @Mike_Bresnahan