Waquar Shah, an officer on duty at the emergency call centre at the time of the attack, told The Associated Press news agency that the attackers was spotted as he climbed over a wall.
"He jumped in from the rear wall, then ran toward the offices," he said. "One of our guys opened fire on him and he fell and blew up."
There have been a number of bombings in cities across Pakistan in apparent retaliation to the army's offensive in North West Frontier Province.
Al Jazeera's Imran Khan, reporting from the scene, said that the emergency response centre hit on Saturday was a "soft target".
"We have seen several of this kind of attack since the operation started against the Pakistani Taliban in the Swat valley," he said.
There was no immediate claim of responsibility for the blast.
On Friday, a suicide bombing at a mosque in Upper Dir, which borders the Swat valley region where the fighting is taking place, killed at least 30 people.
At the end of May, the Tehrik-i-Punjab, a group with links to the Taliban claimed responsibility for a bombing in Lahore that killed at least 30 people and wounded another 200.
The attack targeted a police station and the offices of the Inter-Services Intelligence (ISI), Pakistan's spy agency.
About 15,000 soldiers have been battling an estimated 2,000 Taliban fighters in the Swat valley for more than a month.
Major-General Athar Abbas, a military spokesman, conceded on Saturday that the offensive will not be over until the Taliban leaders have been killed.
"They are the centre of the gravity of this movement, and unless and until they are killed, we cannot declare victory in this whole operation,'' he said.
Abbas said that Maulana Fazlullah, who is believed to lead many of the fighters in Swat, had been "targeted'" three times, but he was unable to confirm reports that he had been wounded.