The US Geological Survey said the 7.8 magnitude tremor struck at 4.17am (local time) at a depth of 17.9km near the city of Gaziantep.
It said on Twitter extensive damage was probable.
The earthquake was felt in the capital Ankara and other Turkish cities, and also across the region.
Reports are coming in that several buildings have collapsed, and a number of people may be trapped.
A BBC Turkish correspondent in Diyarbakir reported that a shopping mall in the city had collapsed.