Temperatures fell below freezing in the early hours of Tuesday as rescuers and relatives picked through the ruins of the building in the city of Konya, 250km south of the capital Ankara.
A two-year-old girl is among the dead. Bystanders cheered workers who pulled out two small girls nearly eight hours after the 36-apartment block buckled at around 8:30pm (1830 GMT) on Monday. So far, 27 people have been rescued.
Agriculture Minister Sami Guclu said rescuers did not know how many people were trapped beneath the rubble.
The cause was not immediately clear. Officials at the scene blamed shoddy construction, while witnesses said they heard an explosion before the building came crashing down.
Some of the survivors were being treated for injuries from jumping out of windows.
As many as 120 people may have been inside. The apartments were crowded with guests coming to celebrate the Eid al-Adha feast, a major Muslim holiday.
Rescue workers said crowds of onlookers were making it difficult to listen for anyone buried alive, including a woman who had used her mobile telephone to call for help.
Nearby residents said there had been structural problems at the building and that its engineers had failed for years to win official clearance to allow people to move in.
Apartments were crowded with
well-wishers for Eid al-Adha
Interior Minister Abd al-Kadir Aksu said: "It's still not clear what caused the building to collapse. Initial reports were that the furnace had exploded, but statements from... officials show it may have collapsed due to an error in its construction."
Civil defence and military units from across Turkey rushed to Konya to assist in the rescue effort.
Similar disasters have in the past been blamed on Turkey's poorly enforced building regulations and shoddy construction.
A derelict wooden house collapsed in central Istanbul on Saturday, killing six people, and 10 students died last June when the dormitory of a Muslim religious college collapsed.
Earthquakes have also taken a devastating toll in Turkey, which is criss-crossed with faultlines.
Poor building standards have been blamed for the high number of deaths in the quakes, including two massive tremors in 1999 that killed more than 18,000 people in Turkey's industrialised northwest.