Fifteen suspects have already been detained over alleged involvement in the plot, Kayseri state prosecutor Mustafa Arslanturk was quoted as saying by Anadolu.
According to Reuters, 12 of the injured are still in in intensive care, while six more are in critical condition.
Television pictures showed that the bus had been reduced to a smoldering wreck by the impact of the blast, as wounded were taken to waiting ambulances.
The explosion comes a week after 44 people were killed in an attack in Istanbul claimed by Kurdish militants.
Anadolu said that the bus was owned by the municipal transport authorities in Kayersi but was transporting Turkish soldiers who had taken permission to go to a local market for the day.
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