McVay revealed on Monday that the 31-year-old defensive tackle had an ankle sprain, although he was still undergoing examination on the severity. He said Rams' medical staff indicated they feared it was a high ankle sprain.
"We're finding that out right now," McVay told reporters about Donald's injury. "He's still meeting with the doctors and getting the necessary scans.
"On Wednesday when we re-convene I'll have a little bit more information for you."
Donald has five sacks, 10 tackles for a loss, 11 quarterback hits and a forced fumble in 11 games this season.
"Obviously we'll take the appropriate steps for Aaron in terms of how we move forward and what that means as far as his availability for this week and the weeks to come," McVay said.
McVay added there was no update on Stafford, who remains in protocol, but rejected talk of shutting down all their star players despite the reigning Super Bowl champions' 3-6 record.
"I think you've got to take each individual case," he said. "As a competitor for those players, you want to be mindful of all the things that go into that. I've always consistently said being smart. They're all factors. We're trying to compete.
"But it's been something nobody could have predicted. When it rains, it pours."
On Sunday, the Rams confirmed wide receiver Allen Robinson II will miss the remainder of the season with a foot stress fracture.