Young's agent, Mark Bartelstein, told ESPN.com that he expects the injury to sideline the veteran for six to eight weeks.
Young suffered the injury while guarding Kobe Bryant during practice Thursday. He underwent an MRI exam Friday that revealed the tear.
"I didn't see it," Lakers coach Byron Scott told reporters Friday before Young's MRI. "He said he tried to swipe at the ball when he was guarding Kobe and his thumb got caught and it swelled up on him."
Young, who averaged a career-high 17.9 points and 1.5 assists per game for the Lakers last season, will have surgery Monday, and the team said a more specific timeline on his return will be given at that time.
The Lakers re-signed Young to a four-year, $21.5 million deal in July.
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