The bombing took place near a security checkpoint in the town of Mingora. At least 30 people were injured.
Reports say that most or all of the dead were civilians.
Government forces have been fighting al-Qaeda and Taleban fighters and tribesmen sympathetic to their cause in the restive region.
Officials told AFP news agency the bomber was trying to approach the checkpoint after bypassing a queue but his car exploded on the way.
TV reports say there is a curfew in Mingora, the region's main town, as security forces launch a fresh search for fighters.
Swat has been the scene of an insurgency since August 2007.
Hundreds of people have been killed since then in battles between security forces and fighters led by Maulana Fazlullah, a cleric with links to the Pakistan Taleban movement.
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