Baas missed the season opener with a knee injury, returned to start in Weeks 2 and 3, injured his neck in the Week 3 loss to Carolina, missed the following three games with that injury, then returned to start Monday only to injure his knee on the opening drive. He did not return.
Baas became the second Giants starting offensive lineman to land on injured reserve this season, joining right guard Chris Snee.
"I really feel like I can't catch a break," Baas said after Monday night's game. "It's definitely frustrating."
Jim Cordle, who has filled in for Baas at center during the past month, is likely to take over as the starting center.
Baas' time with the Giants is likely finished, as he carries a cap number of $8.225 million for 2014 and $8.475 million for '15, and was likely to be cut in the offseason for financial reasons even before the injury.
No corresponding roster move was immediately announced.