The group died from exposure due to the frigid cold, which dropped to -35C (-31F) with wind chill, officials say.
The bodies of a man, a woman, a teenage boy and an infant were found near Emerson, Manitoba, on Wednesday.
US officials say the dead are believed to be a family from India. They are thought to have been attempting to cross into the US.
Manitoba Royal Canadian Mounted Police (RCMP) Assistant Commissioner Jane MacLatchy shared the discovery with reporters in a news conference on Thursday.
"What I am about to share is going to be difficult for many people to hear," she said, calling it "an absolute and heartbreaking tragedy".
Around 09:30 local time (15:30 GMT) on Wednesday, Canadian police were alerted that a US Customs and Border Patrol team had arrested a group that had crossed from the area, which is a known illicit border crossing site.
A US official told the Canadian team that one man was discovered with items for an infant, but that no child was found with him.
A search was launched on both sides of the US-Canada border, and the group was discovered around 13:30 about nine to 12 metres from the US border. Crews using snowmobiles and all-terrain vehicles continued to search the deep snow until late Wednesday evening.
Ms MacLatchy said that the group was "on their own in the middle of a blizzard" and "faced not only the cold weather but endless fields, large snowdrifts and complete darkness".
In a statement later on Thursday, US federal officials in Minnesota announced human smuggling charges against 47-year-old Florida resident Steve Shand.
Mr Shand was found driving a 15-person van in a rural area along the border with cases of food and water in his boot. Two passengers with him were found to be undocumented migrants from India, US officials say.
As they were being transported to a border patrol station, the US agents encountered a group of five Indian citizens who said they had been walking for 11 hours and had been expecting to be picked up by someone.
One of them was carrying a backpack containing children's clothes, toys and medication. He said he was carrying it for a family of four, but they "had become separated in the night".
Based on the description, the bodies found in Canada have been tentatively identified as the family from India, the US statement says. It adds that two other Indian migrants sustained serious injuries and were taken to hospital.
The RCMP's Ms MacLatchy urged "anyone who's thinking of crossing the border in Manitoba, either heading south or north: just don't do it".
"Do not listen to anyone who tells you they can get you to your destination safely. They cannot. Even with proper clothing it is not a journey that is possible."
So-called "irregular" crossings from the US into Canada - crossings outside official border points - increased drastically around 2017, a phenomenon driven by multiple factors including immigration policies put in place by former US president Donald Trump.
Canada banned such crossings at the beginning of the pandemic, with officials turning asylum seekers back to the US. The ban was lifted in November.
Local officials in Emerson say it is rare to see people crossing from Canada southbound into the US.