Swaim had a screw inserted into his foot and will miss the entire off-season program, organized team activities and mini-camp.
It's another setback for Swaim, who missed the final seven games of last season after suffering a torn pectoral tendon.
Swaim, a 2015 seventh-round pick from the University of Texas, was the team's No. 2 tight end behind Jason Witten for the first nine games last season because of his proficiency as a blocker in the Cowboys' two-tight end sets.
He also caught six passes for 69 yards.
Swaim's injury during informal workouts at the The Star this week has made tight end a flashpoint for the Cowboys in the off-season.
Witten is in the final year of his contract. James Hanna missed all of last season with a knee injury, though he should be ready to play.
Rico Gathers, a sixth-round pick who spent last season on the practice squad after a standout basketball career at Baylor, is still a work in progress.
Selecting a tight end to potentially serve as Witten's heir was already a possibility for the Cowboys in the upcoming NFL Draft. The situation might have become even more acute.