It was not clear how many people were inside the building, but rescue workers were digging through the rubble to locate survivors.
Rescue workers told Turkish TV there were sounds coming from under the remains of the building.
Kadir Topbas, the mayor of Istanbul, said it was not immediately clear why the building had fallen.
One neighbourhood official said the building, on Istanbul's European side, was damaged by a deadly earthquake that hit northwestern Turkey in 1999.
Television stations showed pictures of men and women crying around the rubble and sorting through the remains of the building, which were spread out over an entire block.
Earlier this year a woman died when a building collapsed on the outskirts of Istanbul, Turkey's largest city.
Poor construction work and a lack of building regulation and corruption have been blamed for past building collapses.