In a provisional toll released at 5:00 am (0300 GMT), the fire service said six of the dead were children, one of them a baby. Of the injured, 23 were hospitalized, two in serious condition.
The origin of one of the worst blazes in post-war Paris was not known, but a criminal investigation was under way. The inferno swept up the stairwell of the building in the 13th district of the French capital.
The fire was a reminder of a blaze on April 15 this year in the central Opera district in which 24 people, also immigrants, perished in a hotel.
"Two hundred firefighters are at the scene," said a fire brigade spokesman.
Some people tried to save themselves by jumping from windows and others tried to save their children by throwing them from upper floors after the fire broke out in the middle of the night.