Price will be examined Wednesday by team physician Dr. David Mulder to determine whether his headaches are a sign of something more serious. He'll miss Montreal's game against Tampa Bay that night and is doubtful for a game at Carolina on Thursday.
"He needs further evaluation and we're going to give him that," Montreal interim coach Randy Cunneyworth said after practice Tuesday. "I'm trying to be as honest as possible but it's still an ongoing process here. He's still being diagnosed."
Price was struck in the head during practice Thursday when teammate David Desharnais landed on him during a 2-on-1 drill, though Price still made his 65th start of the season in a 4-1 road loss to the New York Rangers the following night.
Price informed the team of his symptoms on Monday.
"Carey usually doesn't stay down very often," Desharnais said. "He was a bit shaken up. I fell right on his head."
The diminutive center fell hard enough that he hurt his ribs from the contact with Price's mask.
"He was complaining a little bit after the practice, just joking around that he had headaches because of me and stuff like that," Desharnais said. "But I guess it's not a joke right now."
Desharnais was relieved to see Price continue with the rest of the practice, which took place while team owner Geoff Molson held a press conference to announce the firing of general manager Pierre Gauthier.
Though Cunneyworth was aware of Thursday's collision, he said he was among the last to learn that Price was not feeling right.
"Davy was doing exactly what we designed the drill to do, getting on top of the goaltender and driving hard to the net," Cunneyworth said.
The Canadiens, who will likely finish last in the Eastern Conference, have not confirmed a report that Price has a concussion. Such a diagnosis would trigger a concussion protocol that would effectively end Price's season.
"You don't automatically go there just because you get a headache," Cunneyworth said. "Obviously you want to go through it if it's truly the case but it is a lengthy process. And right now there are time constraints, but obviously we're not going to mistreat anybody and misdiagnose."
Montreal closes its season with a home game against the Toronto Maple Leafs on Saturday.
Backup goalie Peter Budaj will face Tampa Bay after making a scheduled start in Saturday's 3-2 shootout loss in Washington.
"He doesn't feel really horrible ... but definitely you've got to stay on top of it because it's a dangerous game," said Budaj, who will make consecutive starts for the first time this season.
The Canadiens called up goalie Robert Mayer from Hamilton of the AHL. The club also recalled forward Gabriel Dumont, who will make his NHL debut against the Lightning.