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.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Couple mistakenly served bag of cash at McDonald's drive-thru