About 20 buildings have collapsed, including a six-storey hotel in the city of Van, where dozens of aid workers and journalists were staying.
The quake late on Wednesday was centred 16km (10 miles) south of Van.
The same region was struck last month by a 7.2-magnitude earthquake which killed more than 600 people.
That earthquake struck a little north of Van but the city became the headquarters of the relief effort and has been flooded by aid workers and journalists, says the BBC's Jonathan Head in Istanbul.
The city was only lightly damaged, but some of the weakened buildings are now thought to have been brought down.
Television pictures from Van showed residents and rescuers trying to lift debris to free people trapped under ruined buildings.
Rescue workers were using high-powered lights to work through the night.
Parliamentary member Nazmi Gur said most of the buildings which collapsed were empty, but three had been occupied when the quake struck at 21:23 (19:23 GMT).
He said emergency teams were focusing on rescuing some 50 people believed to still be trapped.
Deputy Prime Minister Besir Atalay said the quake toppled a school and a number of mudbrick homes, as well as the hotel.
He said rescue teams were being sent to the region from the capital, Ankara, and other areas.
Some of the journalists trapped in the collapsed Bayram Hotel had sent text messages to colleagues asking to be rescued, Associated Press quoted a Turkish cameraman as saying.
Alper Kucuk from the Turkish Red Crescent told the BBC that 11 people had been rescued from the rubble of the hotel.
Mr Kucuk said the Red Crescent was sending two more planeloads of relief supplies to the area, including tents and blankets, as well as rescue personnel.
He described it as the biggest aftershock to hit the area and said it had frightened a lot of people.
Thousands of people were made homeless by the 23 October earthquake, with many still living in tents in the cold weather.
Mr Gur said many people are now leaving Van in search of a safer place.
Turkey is particularly vulnerable to earthquakes because it sits on major geological fault lines.
Two earthquakes in 1999 with a magnitude of more than 7 killed almost 20,000 people in densely populated parts of the north-west of the country.
A 5.6-magnitude earthquake has killed at least seven people in eastern Turkey, and trapped many more under collapsed buildings.