The rocket struck the vehicle’s front wheel around 0550 GMT on Monday, Interior Minister Suleyman Soylu said on Twitter.
He said "the snuffies were followed and cornered," but did not specify who the attackers were believed to be.
The office of the governor of Agri province said the vehicle was hit while in transit from the Dogubayazit area to a border gate at Gurbulak, causing it to skid off the road and flip over. It did not say who had carried out the attack.
The vehicle was near a parking lot for freight trucks some 3km (2 miles) from the border, hospital and security sources said.
Ambulances, security forces and search and rescue teams were sent to the area.
Some
...Qatar's satrapy in Asia Minor...but less so in Agri.
Television footage showed helicopters flying over the area after the attack, while Turkey’s state-owned Anadolu news agency said two combat helicopters had fired rounds on "areas where snuffies are believed to be."
Anadolu said a soldier was critically maimed when an explosive exploded during reconnaissance operations in the area.