An MRI revealed a torn tendon, according to ESPN, and the four-time Pro Bowl selection's status for the playoffs remains to be determined.
Johnson, 32, was injured in the fourth quarter of Saturday's 40-34 road loss against the Dallas Cowboys.
Johnson has not allowed a sack since Week 11 of the 2020 season.
Including 15 starts this season, he has started 127 games since Philadelphia drafted him with the No. 4 overall pick in 2013. He is a four-time Pro Bowl selection.
The Eagles (13-2), who can clinch the NFC's No. 1 seed with one more win, finish the regular season with home games against the New Orleans Saints this Sunday and the New York Giants on Jan.