Officials said a time bomb attached to a motorcycle exploded in the crowded Khyber bazaar in central Peshawar on Tuesday.
Habibur Rehman, the city's chief of police, said the blast happened as the city was on high alert after threats to the US consulate.
"It was a time bomb which exploded when the market was full of customers," Rehman said. "One policeman who was passing by was killed and 16 other people were hurt.
"The security was tight particularly around the consulate and government buildings, but the terrorists chose to strike a market place.
"There is a possibility that the terrorists wanted to strike at a different place but because of the tight security they detonated the device in the bazaar."
A spokeswoman for the US embassy in Islamabad said earlier that the Peshawar consulate had closed "because of information about a specific and credible threat".
"The consulate in Peshawar is working with Pakistani authorities to co-ordinate increased security measures," Nida Emmons said.
A Pakistani security official said the consulate closed after an official at the mission received a threatening telephone call.