Henry will be examined by a hand specialist on Monday, the Lakers announced Saturday night.
Henry was injured in Friday's game against Washington, and an MRI revealed the tear. He scored 12 points while playing more than 23 minutes against the Wizards.
Injuries have badly hindered Henry's otherwise successful first season with the Lakers.
Henry is averaging 10.1 points and 2.8 rebounds, but only returned March 3 after a 28-game absence with a right knee injury. He had been out since Dec. 29.
Kobe Bryant and his struggling Lakers have been battered by injuries all season. Steve Nash, Jordan Hill and Nick Young returned from absences Friday.
Los Angeles hosts Orlando on Sunday night.