"The president said that the perpetrators of such a heinous crime would be brought to justice," a statement from Zardari's office said.
Police in the region were said to have been put on high alert before the attack.
"We had intelligence reports that a car bombing could take place in any of three districts of the province," Malik Naveed, a provincial police chief, said.
Charsadda district is 35km north of Peshawar, the capital of the restive North West Frontier Province, on the Afghanistan border.
The province is an area of activity and refuge for pro-Taliban and al-Qaeda fighters who have increased their attacks in the past two years.
Charsadda borders the Malakand division which includes the Swat valley, where a government accord was signed on Monday allowing a stricter interpretation of sharia (Islamic law).
The state made the move in an attempt to bring under control a long-running conflict with tribal groups in the region.