Cowboys executive vice-president Stephen Jones said the team was awaiting MRI results after the injury Sunday but feared it could be a season-ending tear.
Crawford went down during non-contact individual drills. He pounded the ground in anger and covered his face with his hands as he was taken off the field in a cart.
The second-year player is a backup who is listed as an end but can play tackle. He thanked his fans on Twitter, writing that their support was "very much needed right now."