Civilians may have also been wounded in the blast, it said.
A vehicle rigged with a bomb exploded next to the bus -- which was transporting off-duty soldiers, according to the country's Anadolu state news agency. The blast happened near Erciyes University in the central province of Kayseri, according to a tweet from Anadolu.
Turkey's President Recep Tayyip Erdogan and Prime Minister Binali Yıldırım are being briefed on the situation, according to the news agency.
A video showed a decimated bus with smoke rising out of the vehicle.
Immediately after the blast, at least a half dozen ambulances arrived on the scene. Images showed people with head wounds and at least one person being taken away on a stretcher.
The attack came exactly a week after a pair of bombings in Istanbul killed 44 people, including 37 police officers, and injured 155 others. The two explosions last Saturday occurred after a heavily attended soccer game at Besiktas Vodafone Arena.
A Kurdish militant group called the Kurdish Freedom Hawks claimed responsibility for last week's bombings. It stated on its website that the Turkish people were not the target of the attack.
The latest violence follows a wave of deadly bombings that have struck Turkey this year.