A city worker who chanced to walk by shortly after midnight saw the building swaying and alerted people inside by shouting and throwing stones at the windows, said Istanbul Mayor Kadir Topbas.
Some people managed to safely flee, but the dead and injured had become trapped on a stairway as the building toppled, said Ali Karahan, chief of Istanbul firefighter department.
Rescuers pulled out the body of a woman from the rubble, while another woman died of her injuries in hospital, the Istanbul mayor's office said.
Istanbul Gov. Muammer Guler said that a 7-year-old girl who was believed dead had been taken to hospital where doctors found she was still breathing.
"She is alive and connected to a respiration machine,' Guler said. Her face had been covered in dust when she was pulled out.
It wasn't clear how many people were inside when it came down. Guler said at least 27 people were living there and several people were in a coffee shop in the basement.
There was no immediate word on the condition of the injured.
Rescue teams with sniffer dogs worked under floodlights to find out whether there were any others trapped under the rubble.
"We think maybe just a few more people remain buried,' if there is anyone left inside, Guler said.
Officials blamed the collapse in residential Zeytinburnu district on shoddy construction but did not provide details Topbas said that the building was listed as among those that needed to be demolished because their ability to withstand a strong earthquake was questionable.
Such collapses in Turkey are sometimes associated with earthquakes, a constant worry for residents of this sprawling city of more than 12 million.
Geologists have urged the Turkish government to tear down some 50,000 buildings that would probably collapse if a big quake hits Istanbul.
They say hundreds of thousands of other buildings that rise in an unstable mass of brick, mortar and stone, need to be reinforced.
Topbas said the collapsed building was on the list of 16,000 other buildings marked as unsafe and needed to be pulled down in Zeytinburnu district alone.
