The veteran center will be placed on injured resereve, the team announced Wednesday.
The Boston Globe's Greg A. Bedard originally reported the news.
Koppen suffered the injury against the Dolphins in Week 1. It was at first reported to be a broken ankle that would sideline him for six to 10 weeks. ESPN then reported last week that Koppen actually broke his fibula and would undergo surgery that would keep him out eight to 10 weeks.
Dan Connolly has filled in for Koppen, and the Patriots' offense hasn't slowed down yet. New England leads the league in yards gained and is third in points scored.
Koppen was a fifth-round pick in 2003 and made the Pro Bowl in 2007.
The report also said defensive lineman Myron Pryor will be placed on IR.