Gesicki suffered the injury during a drill on Monday and was seen grabbing at his shoulder as he headed toward the locker room.
After five seasons in Miami, the Patriots signed Gesicki to a one-year, $4.5 million contract in March worth up to $9 million with incentives.
The pass-catcher is pegged for a sizable role in New England’s reworked offense in two tight-end sets alongside Hunter Henry. With the dearth of dynamic wide receivers in New England, the 6-foot-6 TE could be a significant factor in the Patriots’ passing game, including the red zone.
After being miscast in Mike McDaniel’s offense last season in Miami, Gesicki was set to return to the pass-catching role he thrived in early in his career. The hope is the shoulder issue won’t derail that plan before it gets off the ground.