The accident occurred in snowy, slippery conditions Sunday afternoon in Gammelstad, the Swedish news agency TT reported.
Both vehicles burst into flames.
"The car was driving at high speed and went right into the bus, according to witnesses," Tomas Wikstrom of the emergency services in Lulea told TT.
The car's driver was pronounced dead at a hospital.
She had been driving on the wrong side of the road, police said.
"It was like in a film, I just saw how everything lit up in front of me and then 'bang.' I flew to the ground and hit my head," said bus passenger Sanna Anehagen. "There were small children on the bus and they started crying, everyone was in shock."
Ten of the 15 people on the bus were injured, including the driver.
"It's quite cold and there has been a great deal of snow, so it may have been this," Wikstrom.