The Mounties said the bodies of two men, both aged 28, and a woman, 25, were discovered after the fire was brought under control on the Siksika Nation on Saturday morning.
Police said neighbours called RCMP after noticing smoke coming from the windows.
Tom Littlechild, the director of emergency services for the Siksika Nation, said flames were already coming out the windows of the kitchen and living room windows by the time the community's firefighters arrived.
Littlechild said the firefighters called for extra help from the fire department in the neighbouring community of Cluny, and they were able to put the flames out quickly. When they got inside, a man and a woman were discovered in one bedroom, and the other man was discovered in another bedroom.
"The fire, the bulk of it, was on the east end of the house where the kitchen and living room were. The bedrooms, for all intents and purposes, were not really touched by flames at all," Littlechild said.
There were no reports that anyone else was in the house at the time of the fire, Littlechild said.
He said the home did not have a working smoke detector.
RCMP, the Siksika Nation fire department and the Cluny fire department are still investigating the cause of the fire, but police said in a news release the blaze appears to have started inside the home and doesn't appear suspicious.
The release said the three victims were all residents of the Siksika Nation and had only recently moved into the house.
Their names haven't been released and police said they are contacting their families. Autopsies will be performed in Calgary next week, the release said.
The Siksika Nation, which is about an hour's drive east of Calgary, is home to approximately 7,000 people. It was hard hit when the Bow River spilled its banks in June 2013 and about 170 homes were flooded.
Littlechild said he doesn't recall a fatal fire in the community in over five years.
He said he didn't know the victims of the fire personally, but he said counselling would be available for other members of his department.
"Even though it's a tragic event, the positive thing I guess to try to get across to everyone is the importance of having a working smoke alarm in your home," Littlechild said.