The 6.0-magnitude quake, centred on the village of Basyurt in Elazig province, struck at 0432 (0232 GMT). It has been followed by more than 40 aftershocks.
Officials said the nearby village of Okcular had been almost destroyed and several others badly damaged.
A number of people were trapped in the rubble of collapsed buildings, many of which were built of mud-bricks.
"Villages consisting mainly of mud-brick houses have been damaged, but we have minimal damage such as cracks in buildings made of cement or stone," Elazig Governor Muammer Erol told CNN Turk.
At least 17 of the dead came from the hillside village of Okcular, where up to 30 houses collapsed, rescuers said.
"The village is totally flattened," Okcular's administrator, Hasan Demirdag, told NTV.
Television footage from Okcular showed rescue workers and soldiers digging among the rubble of collapsed buildings as villagers looked on.
Ali Riza Ferhat, a resident, said he had been asleep in his home when the earthquake struck.
"I tried to get out of the door but it wouldn't open. I came out of the window and started helping my neighbours," he told NTV. "We removed six bodies."
The nearby villages of Yukari Kanatli, Kayalik, Gocmezler and Yukari Demirci were also badly damaged and each reported several deaths.
"Everything has been knocked down - there is not a stone in place," Yadin Apaydin, the administrator for Yukari Kanatli, told CNN Turk.
At least 50 people have been taken to hospital, officials say. Some were reportedly hurt during the panic after the first earthquake, when they jumped from windows or balconies.
Residents of the affected villages have been warned not to return to damaged homes while the area continues to be hit by aftershocks, the strongest of which have so far measured 5.1 and 5.5.
The government disaster management centre and Turkish Red Crescent have set up tents to help survivors cope with the harsh winter weather, and are also distributing food and blankets.
Deputy Prime Minister Cemil Cicek and three other ministers have travelled to the earthquake zone to provide assistance.
In Ankara, Prime Minister Recep Tayyip Erdogan lamented the lack of earthquake-safe buildings and said he had ordered the start of a reconstruction project in the area.
"Mud-brick construction is undoubtedly a local tradition. But unfortunately, it has proved to have a heavy price," he said.
A BBC News website reader who visited the village of Basyurt after the earthquake said its residents blamed the government for the destruction and loss of life.
"This is a seismic area. We've experienced so many earthquakes in the last 20 years, yet no measures have been taken to strengthen the buildings," Volkan Durkal said.
"Most houses are not made with cement, they are not well-built and the people are not well-educated about what to do and where to take cover during an earthquake."
Turkey is plagued by earthquakes - generally minor - because of its location on the North Anatolian fault line.
A 7.4-magnitude tremor which hit the western city of Izmit in August 1999 killed more than 17,000 people.
The BBC's Jonathan Head in Istanbul says poor quality buildings were also blamed for the high death toll then and there is still concern in Turkey's largest city, where seismologists predict a major earthquake will occur within the next few decades. BBC