The reason for the collapse on Thursday was not immediately known and an investigation was under way.
Rescue teams were working to reach those trapped even as there were warnings of a further collapse of the building.
The building's three lower floors, including a ground-floor shop, caved in before dawn in the district of Maltepe, on the Asian side of Istanbul, a city that is bisected by the Bosporus Strait.
Residents from the upper floors were safely evacuated while search teams rescued eight more people from the rubble.
The rescuers recovered two bodies and were trying to reach two people still believed to be inside, according to the Istanbul governor's office.
Earlier, Davut Gul, the governor of Istanbul, said rescuers had made contact with a six-year-old trapped in the rubble.
It was not immediately clear if the child was among those rescued.
He warned that the building was at risk of further collapse, hampering the rescue efforts.
Nearby buildings were also evacuated for safety, the governor said.
Istanbul and other parts of Turkey are undergoing an urban transformation program that aims to replace old and earthquake-risky buildings with safer housing.
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