Clash brings death toll to 45 in four days in battle against Pakistani Taliban.
Muntizar Hassan, a police officer, said that Kazmi had survived the attack but that his driver had been killed.
Kazmi was said to have been shot in the leg. A bodyguard was also wounded in the attack.
Television pictures showed several bullet holes in the vehicle.
Kazmi, who belongs to the Barelvi sect of Sufi Islam, has been a vocal critical of the Taliban in Pakistan.
The Pakistani army launched a campaign in April to clear Taliban fighters from Swat and Buner, two valleys a few hours drive from Islamabad.
Pakistan’s major religious parties quickly moved to condemn the attack on Kazmi.