It was not clear how many people were inside when the building came down. Muammer Guler, the Istanbul governor, said at least 27 people were still living there at the time.
Rescue teams with dogs dug survivors out of the rubble after the building fell shortly after midnight.
Guler said 26 people had been rescued and were being treated in hospital, among them a seriously injured child.
He said: "We think maybe just a few more people remain buried."
Ali Karahan, chief of Istanbul's fire department, said some residents managed to escape when the building began crumbling and those who were injured were all trapped in the stairwell.
A municipality worker and the owner of a coffee shop in the basement of the building, alerted the residents by ringing the bells, shouting and throwing pebbles at the windows, saving many lives, the authorities said.
A municipality worker who was walking in the street by chance saw the building rocking and alerted the residents by shouting and throwing stones at the windows, Topbas said.
|The building was one of 16,000 in Zeytinburnu|
district that need to be demolished [EPA]
Ilhan Karadeniz, the owner of the coffee shop, said he woke up his neighbours when he noticed that the building was shaking.
Witnesses told Turkish television the building had been damaged in the earthquake in 1999 which killed about 18,000 people west of Istanbul. Media reports suggested that its foundations might have been weakened by an adjacent construction.
Corruption, lack of building regulations and shoddy construction have been blamed for building collapses in Turkey in the past.
Poor construction was also blamed for many of the deaths in two 1999 earthquakes in western Turkey. Experts say little has been done to address the problem.
Several contractors who were charged with negligence for ignoring building codes escaped punishment this week when statute-of-limitations expired in all ongoing cases that were filed in 1999.