Those hurt included about 30 soldiers as well as civilians and high school students.
Mutlu said the car bomb had been set off by remote control as a
military vehicle was passing, about 100m from a military base and billets.
He said bomb experts were looking for clues at the scene.
Al Jazeera's Yusuf al-Sharif, speaking from Ankara, said a large number of passengers were burnt to death inside the bus before rescue workers managed to pull them out.
Police threw a security cordon around the scene and kept reporters away, saying this was a precaution against a possible second explosion.
Two of the five victims were high school students attending private lessons at a nearby building.
Officers said they were looking for two people that witnesses had said they had seen fleeing the scene, but it was not immediately clear whether they were suspects.
Recep Tayyip Erdogan, Turkey's prime minister, and the US embassy in Ankara condemned the blast as a "terrorist act".
Speaking on television, Erdogan said: "Terrorism has reared its ugly head again. But these incidents will not affect our determination to fight terrorism both at home and abroad."
In a statement the US embassy condemned the blast as "a horrible example of the meaningless tragedies caused by terrorism".
It said the US "reiterates its determination to stand by Turkey in the struggle against all kinds of terrorism".
Diyarbakir is the biggest city of mainly Kurdish southeast Turkey and home to large numbers of troops who are battling the Kurdistan Workers' Party (PKK) both inside Turkey and in nearby northern Iraq.
Thursday's attack came a day after an explosion in Turkey's commercial centre, Istanbul, left at least three people injured.
The blast in a rubbish bin occurred on Wednesday in Kucukcekmece district, the same area where a homemade bomb went off last week, also in a rubbish bin, killing a woman and injuring half a dozen people.
Tensions in the country are running especially high because Turkey has been carrying out cross-border military strikes in northern Iraq aimed at the PKK.
The PKK had said recently that it would retaliate against the attacks.