Osman underwent further testing Saturday in Los Angeles, a day after he left the team's 116-102 loss to the Clippers.
The Cavaliers said their backup forward will begin treatment and rehabilitation and his specific return date will be determined upon reassessment.
Hood played seven minutes in the first quarter against the Clippers before exiting with the injury, finishing with zero points on 0-for-3 shooting.
Jeff Green will start in Hood's place against the Lakers, Lue said.
Information from ESPN's Dave McMenamin was used in this report.