The reigning Heisman Trophy winner was hurt just before halftime Saturday in the third-ranked Sooners' season-opening 14-13 loss to No. 24 Brigham Young when he was flattened by linebacker Coleby Clawson.
Stoops said he would know more after Bradford's MRI examination Monday.
Bradford watched the second half of the BYU game with his left arm in a sling and an icepack.
In his absence, backup Landry Jones, a red-shirt freshman, completed 6-of-12 passes for 51 yards.