The magnitude 6.8 quake shook Elazig province, about 550km east of the capital Ankara, and was followed by dozens of aftershocks.
Thirteen people were killed in Elazig and five more in the neighbouring province of Malatya, Health Minister Fahrettin Koca said after rushing to the region with other ministers to oversee the rescue operation.
Interior Minister Suleyman Soylu said emergency workers were searching for 30 people under the rubble, and more than 500 people were injured.
State broadcaster TRT showed footage of police and emergency workers searching a partly collapsed building in Elazig. Windows were smashed and balconies had crashed to the ground.
At another collapsed building, teams worked with their hands to remove bricks and plaster from the ruins. Elsewhere emergency workers used drills and mechanical diggers to clear the debris, while injured people were taken on stretchers to ambulances.
Soylu described the earthquake as a "Level 3" incident according to the country's emergency response plan, meaning that it called for a national response but did not require international help.
He said Turkey, which straddles seismic faultlines and is prone to earthquakes, had learnt lessons from previous disasters which helped it address Friday's incident. Drones were deployed in search operations and communication between provinces.
Turkey's Disaster and Emergency Management Authority (AFAD)warned residents not to return to damaged buildings because of the danger of further aftershocks. It said beds, blankets and tents were being sent to the area, where the overnight temperature was below 0 degrees Celsius.
State media in Syria and Iran both reported the earthquake was felt in those countries. Local media in Lebanon said the cities of Beirut and Tripoli also felt the quake.
Turkey has a history of powerful earthquakes. More than 17,000 people were killed in August 1999 when a 7.6 magnitude quake struck the western city of Izmit, 90 km (55 miles) southeast of Istanbul. About 500,000 people were made homeless.
In 2011 an earthquake struck the eastern city of Van and the town of Ercis, some 100 km (60 miles) to the north, killing at least 523 people.
