Stork, who sustained the injury in the second quarter of the divisional-round win over the Ravens, did not practice all week.
A 2014 fourth-round draft choice out of Florida State, Stork has started 12 games this season (including playoffs) and his insertion into the starting lineup in late September helped stabilize the offensive line after a rocky start to the season.
Veteran Ryan Wendell, who started at center for the Patriots in 2012 and 2013, is expected to take over for Stork.
Wendell has been the team's right guard this season, so if he shifts to center as expected, it creates a void at right guard that second-year player Josh Kline is the leading candidate to fill. Rookie Cameron Fleming is another possibility at right guard.