The attack late on Saturday was blamed on Kurdish rebels, and came a day after Turkey launched air strikes against Kurdish insurgents in northern Iraq.
Following the incident Turkey called a special meeting of Nato ambassadors to discuss military operations against the Islamic State (IS) group and PKK Kurdish separatists.
The meeting will take place tomorrow.
The Kurdish rebel group, the Kurdistan Workers’ Party, or PKK, said the air strikes likely spelled the end of a ceasefire announced in 2013 by then Turkish premier, now president, Recep Tayyip Erdogan.
Turkey has simultaneously bombed Islamic State positions in Syria near the Turkish border and carried out widespread police operations against suspected Kurdish and IS militants and other outlawed groups inside Turkey. Hundreds of people have been detained.
The private Dogan news agency said Turkish artillery near the south-eastern town of Semdinli shelled PKK targets across the frontier in northern Iraq for three hours early yesterday.
The car bomb on Saturday exploded on a road in the town of Lice as a vehicle carrying military police officers was travelling to intervene against Kurds who had blocked a main intersection and set cars on fire, said the governor’s office in Diyarbakir, a mainly Kurdish province.
The military said the PKK militants also detonated a roadside bomb and fired on the troops in the attack it called a “treacherously pre-planned” ambush.
The military statement said a large-scale operation was underway to capture the attackers.
Assailants also fired on police stations in the cities of Diyarbakir, Siirt and Mardin. No-one was injured in the attacks.
The PKK has fought Turkey for autonomy for Kurds in a conflict that has claimed tens of thousands of lives since 1984.
On Saturday, Turkish fighter jets struck Kurdish rebel shelters and storage facilities across the border in northern Iraq, Turkey’s first such strikes since the peace process with the Kurds was launched in 2012.
A cease-fire was announced the following year.