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.
At least 17 of the dead came from the hillside village of Okcular, where up to 30 houses collapsed, rescuers said.
Television footage from Okcular showed rescue workers and soldiers digging among the rubble of collapsed buildings as villagers looked on.
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.
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