Emergency response officials say all four are believed to be in their 20s.
Crews were called about 6 a.m. to the blaze on the Tsuu T’ina (soo-TEEN'-ah) reserve, which abuts Calgary's southwest city limits.
Redwood Meadows fire Chief Rob Evans says the house was destroyed.
He says it will take a lot of work to determine exactly what happened.
Evans says he would like to see fire chiefs push the message that sprinkler systems in homes are important, especially in rural areas, which crews can’t easily get to.
He says there have been far too many tragic fires recently.
Two young children recently died last month in a fire on a reserve near Loon Lake in northern Saskatchewan. A two-year-old boy and his 18-month-old sister were at their grandmother's house.
The chief of the Makwa Sahgaiehcan (Sah-GAYG'-gehn) First Nation said his reserve has a working fire truck, but not enough money for proper equipment or to train crews.
The volunteer fire department in nearby Loon Lake was called but didn't respond, because service to the reserve had been cut weeks earlier over unpaid bills.
The bills have since been paid and a new service agreement is in place.
Last week, four brothers died in a house fire in the tiny community of Kane, Man. Their mother escaped with three of their siblings, but the boys were sleeping on the second floor of a two-storey farmhouse and could not get out.