The attacker crashed his cycle close to a police van on the busy University Road, Geo News reported.
The report quoted an official as saying the city's police commissioner appeared to be target of the attack but he escaped unhurt.
Killings have escalated as Pakistanis prepare to vote in next month's election to pick the next government.
On Sunday, eight people died and 29 were injured in bombings at election offices near Peshawar and in Orakzai Agency.
Most attacks have targeted Pakistan's secular parties.
CNN reported the Pakistani Taliban took responsibility for Sunday's bombings, saying one cannot be secular and Muslim at the same time.
In an earlier video, Pakistani Taliban leader Hakimullah Mehsud asked people to stay away from the elections.
"We want the implementation of Sharia [the legal code of Islam] and for that jihad is necessary," he said.