Rodney Hood also won’t face the Lakers and is considered day-to-day.
Both players were injured in Cleveland’s 116-102 loss to the LA Clippers on Friday.
Osman, the team’s backup small forward, had three points and a steal in 11 minutes before straining his left hip and leaving the game in the third quarter.
Hood, the Cavs’ starting small forward, played seven minutes in the first quarter before exiting with a strained back, finishing with zero points on 0-for-3 shooting.
Jeff Green will start in Hood’s place against the Lakers, coach Tyronn Lue said.
Information from ESPN’s Dave McMenamin was used in this report.