The police say the officer, Rao Anwar, was unhurt in the attack, which took place late on Tuesday. The bomber had an unknown number of accomplices who opened fire at Anwar’s car after the explosion. His guards returned fire, killing two of the gunmen.
The police have mounted a hunt for the rest of the attackers.
On Wednesday, Pakistani Taliban spokesman Mohammad Khurasani claimed responsibility for the attack.
The Taliban have been waging a war on the Pakistani government for years, a conflict that has killed tens of thousands of people over the last decade.