Many of the people who were injured in the bomb attack remained buried under rubble and only eight bodies had been recovered, Subhan Khan, a senior police officer said.
The growing violence is adding to a sense of urgency for Pakistan's fragile coalition government to end the political infighting and turn its attention to security and pressing economic problems.
Al Jazeera's Mike Hanna in the Swat Valley, said: "The security situation threatens to spiral out of control and militans are seizing the opportunity to fill in the vacuum created by the political division among those supposed to govern."
Two policemen were also injured after a bomb planted in a bicycle exploded near Saddar police station in Karachi, police said.
Fighters were also reported to have killed two civilians and wounded three children in a bomb attack near a security checkpost in Barikot to the west of Mingora, the valley's main town.
The valley had been one of the country's main tourist destinations until last year when Pakistani Taliban fighters infiltrated from enclaves on the Afghan border.
Violence subsided in Pakistan when a coalition government came to power after elections in February and opened talks with fighters.
Authorities in the North West Frontier Province reached a peace deal with fighters in the Swat Valley in May, but attacks had intensified again across the northwest, including the Swat Valley, after Baitullah Mehsud, a Pakistani Taliban leader, suspended talks in June.