Price left the morning skate early Wednesday and did not return.
"It's a lower-body injury that he aggravated during the Olympics," coach Michel Therrien said. "We want to ensure that he's completely healthy when he returns to the lineup. His situation is one that we'll be evaluating day by day. We'll check on his status for practice on Friday ahead of the game on Saturday [vs. the Toronto Maple Leafs]."
Red Wings coach Mike Babcock, who was behind the bench for Canada in Sochi where it won the gold medal, said he was unaware of any injury bothering Price.
"All I know is he played really well for us," Babcock said.
Price, who was named the top goaltender of the Olympic tournament after going 5-0-0 with an 0.59 goals-against average, .972 save percentage and two shutouts, reportedly faced one shot on a 5-on-0 power-play Wednesday and got up favoring his leg.