Locals in Inukjuak, 900 miles (1,500 km) north of Montreal, say the whales are breathing through a hole in the ice.
Fisheries and Oceans Canada said it is sending a team on Thursday to evaluate the situation.
A hunter in the area first spotted the whales on Tuesday, a day after locals say the bay froze.
Dozens of villagers made the one-hour snowmobile ride on Tuesday to see the whales.
“It appears from time to time that they panic,” Mayor Peter Inukpuk told broadcaster CBC.
“Other times they are gone for a long time, probably looking for another open space, which they are not able to find.”
Inukjuak’s public safety officer told CTV’s website that the whales should not even be in the area in January.
“We’ve only seen those kind of whales in the summer time, never in the winter time,” Simeonie Nalukturuk said.
Several villagers said the hole appeared to be shrinking as the ice froze further.
Peter Inukpuk has asked for an icebreaker to free the whales – the Fisheries and Oceans Canada said it was still considering the situation.
“Fisheries and Oceans Canada is assessing the situation and are exploring every possible option, but will only be in a position to determine what – if anything – can be done once our specialists arrive on site,” spokesman Frank Stanek said in a statement.
A spokeswoman for the department told the CBC that icebreaker ships were “really busy with the ice conditions that we have in other regions of our country”.
She added that three commercial ships had become stuck in ice along the St Lawrence River in Quebec this week.
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