The bomb targeted a police van on the main road at Gulbahar area, police officials and witnesses said.
The police van was destroyed by the blast. Several other vehicles were also damaged.
The injured were taken to a nearby hospital, where a policeman succumbed to his injuries.
Officials described the condition of two injured policemen as critical.
The road was closed for traffic after the blast.
Officials said the police van was taking prisoners to a court in another city when it was attacked.
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It was unclear if any militants were among the prisoners.
No group claimed responsibility for the attack though such incidents are usually blamed on the Taliban.
This was the second bomb attack in two days that targeted police in Peshawar, the capital of Khyber-Pakhtunkhwa province.
A senior police officer escaped unhurt in a roadside bomb attack yesterday.