The armoured minibus was carrying detainees accused of "terror" crimes when the car bomb exploded in the centre of Diyarbakir, the office of the regional governor said in a statement.
The state-run Anatolia news agency blamed militants from the outlawed Kurdistan Workers Party (PKK) for the attack.
The seven detainees were being taken for a routine health check after being detained earlier on suspicion of membership of the PKK.
Forty-five people, 12 police and 33 civilians, including people who had been sitting in a tea garden by the roadside, were wounded in the initial blast, the statement said.
Three people later died of their wounds in hospital, it added, without specifying if police or detainees were among the fatalities.
Pictures from the scene showed the blast had left a trail of devastation with the bus reduced to a burned out wreck and its debris strewn around the area.
Bystanders led bloodied survivors to safety.
Diyarbakir and its region have in recent months been hit by repeated attacks by the PKK as the military presses a relentless offensive against the Kurdish militants.
Earlier, two police had been killed in a bomb attack blamed on the PKK in a district of the southeastern city of Van to the east which had so far been spared the worst of the fighting.
Seven Turkish police officers were killed and at least 27 people wounded in late March in a bomb attack on their vehicle in Diyarbakir.
The PKK first took up arms in 1984 demanding a homeland for Turkey's biggest minority, later paring back its demands to focus on cultural rights and a measure of autonomy.
Over 40,000 people have been killed in the insurgency.
The new upsurge of violence between the security forces and Kurdish militants erupted in July 2015, shattering a two-and-a-half year truce.