Follow-up X-rays were negative on Tagovailoa's ribs, and the second-year quarterback's availability for Week 3 and beyond will be determined based on his pain tolerance, the source said.
Dolphins coach Brian Flores said Monday that Tagovailoa was still "in a good deal of pain" and was still undergoing testing. He said Tagovailoa was day-to-day.
The Bills came out aggressive to start the game, pressuring Tagovailoa on four of the six snaps he took, including two sacks on Miami's opening drive.
He was replaced in the 35-0 loss by Jacoby Brissett, who finished 24-of-40 passing for 169 yards and an interception, which Flores said Sunday was "not good enough" -- a descriptor he applied to Miami's entire team, himself included.
NFL Network first reported the news of Tagovailoa's negative X-rays.
ESPN's Marcel Louis-Jacques contributed to this report.