The institute said the earthquake struck at 1041 GMT and was 5 km deep.
Some buildings collapsed and emergency teams were trying to rescue people believed to be trapped in a building in Van, near the Iranian border, state-run news agency Anatolian said.
It said 50 injured people had been taken to hospital in Van, but did not give details on how serious their injuries were.
Television pictures showed damaged buildings and vehicles, crushed under falling masonry, and panicked residents wandering in the streets.
Turkish media said phone lines and electricity had been cut off. Prime Minister Tayyip Erdoğan will head to Van to see the damage, media reported.
Aftershocks continued after the initial quake, whose epicentre was at the village of Tabanlı, north of Van city, the agency said.
In Hakkari, a town around 100 km south of the city of Van in southeastern Turkey, a building could be felt swaying for around 10 seconds during the quake.
There was no immediate sign of any casualties or damage in Hakkari, around two and half hours drive through the mountains from Van, around 20 km from the epicenter.