Carolina running back Fozzy Whittaker went into concussion protocol shortly after Stewart's injury.
Rivera said backup safety Dean Marlowe aggravated his hamstring injury against the 49ers, adding "that didn't sound good, either".
The ninth-year RB underwent a MRI Monday morning, but results are unknown at this time.
The Panthers announced Stewart would not play in the second half after leaving early in the first half against the 49ers. He did not return, finishing with 9 yards rushing on five carries. Fozzy Whittaker and Mike Tolbert both replaced Stewart on rushing duties, Whittaker had 100 yards rushing.
"If Jonathan's (injury) is prolonged, then we'll certainly have the opportunity to see Cameron Artis-Payne out there", Rivera said. He sat out Sunday's contest as one of the inactives, but Rivera spoke after the game about the young running back and using him in Stewart's absence.
Rivera said that while anything is possible, he did not sound as though the team would bring in a running back from outside the organization.