His availability for the rest of season is now in question with the injury, which he sustained during the fourth quarter of Sunday's 20-19 win over the Cincinnati Bengals.
The Cowboys said Bryant -- who leads the team with 75 catches, 1,028 receiving yards and nine touchdowns -- is to visit a hand specialist to determine if surgery is required.
If so, he is likely to miss the rest of the season as the Cowboys (7-6) battle to catch the New York Giants (8-5) for the NFC East championship or land a wild card spot.
His status for Sunday's game against Pittsburgh is undetermined.
Swim Week Miami Beach 2014 [PHOTOS]