Three other people were injured in the blaze late on Saturday in Rinkeby, a suburb of the Swedish capital. Police say the victims were found in a stairwell.
The cause of the fire was not immediately clear but investigators say they believe it was an accident.
Swedish media reported that the woman and her daughters, ranging from a baby to a girl in her teens, lived in an apartment above the fire. They apparently tried to escape down the stairwell even though it was full of smoke.
"If the mother and the children had stayed in their apartment instead of fleeing into the stairwell, they would most likely have survived," rescue spokesman Christer Angehov was quoted as saying by TV4.
Rescuers said the fire was limited to one apartment, but other apartments in the five-floor building sustained smoke and water damage.
