The team announced the change on Saturday. Finnegan had been listed as questionable on Friday after missing three straight days of practice.
Sunday's game will be the third straight Finnegan has missed since hurting his right hamstring in a loss against the New York Jets on Sept. 27.
Nick Harper already was out after breaking his right arm last week in a 31-9 loss to Indianapolis.
Defensive back Vincent Fuller, who broke his right arm, practiced and is questionable. He has not been cleared yet for contact.
Rookie Jason McCourty likely will make his second straight start.