Anderson was escorted off the field after he was sacked by Kyle Van Noy with 1:25 remaining in the Bills' 25-6 loss to the New England Patriots on Monday night.
Anderson took over the starting job in Week 7 after Josh Allen suffered an elbow sprain.
With Anderson and Allen both injured, the Bills could use a backup quarterback -- unless Terrelle Pryor, expected to sign Tuesday, can play that position again while learning the playbook on the fly.
Allen has been officially ruled out against the Bears.