Anderson was hurt was he was sacked by Osi Umenyiora. He walked off the field and went to the locker room for further examination. He was replaced by Brady Quinn.
Anderson was 4-of-10 for 20 yards.
Two other Browns were also injured in the game. Safety Brodney Pool was being evaluated for a concussion and kick returner Joshua Cribbs hurt his left ankle.
The Giants also had three players injured.
Anthony Wright, the backup quarterback, left the game late in the second quarter with an apparent back injury after he was hit from behind by Cleveland's Michael Adams.
Reserve running back Kay-Jay Harris injured an ankle with just over 2 minutes left in the game and was taken off on a cart. New York wide receiver Brandon London injured a shoulder.