The fire started at about 4:30 a.m. in the downtown area of the southwestern city, Today's Zaman reported.
Police spokesman Klaus Hinderer told news agency DPA that 13 people were registered as living in the building, but it was unclear as to how many people were there when the fire started.
Eight people were killed in the fire, police said, including seven children, ages 17, 14, 8, 7, 6, 3, and 6 months. The mother of the children, 40-year-old Nazli Ozcan Soykan, was also killed in the fire. Three other people were injured and taken to the hospital.
Earlier news reports said seven people perished in the fire, but Backnang mayor Frank Nopper confirmed that the death toll is eight.
Police said they believe the fire was started in a second floor apartment and that they are focusing their investigation on a heater in the unit. The building was a former leather factory and now contains several apartments, police said.
Property damage caused by the fire, which spread to neighboring shops, was estimated to be more than $100,000, Bild newspaper reported.