Two accomplices of the bomber were arrested, Aftab Ahmed Khan Sherpao, Pakistan’s interior minister, said.
Police sealed off the airport soon after the blast, but the remains of a body could be seen in the car park through a fence, a witness said.
Al Jazeera's correspondent Kamal Hyder said flights had been disrupted as all airport gates had been closed but flights had since resumed.
Pakistan has been left reeling by a string of suicide attacks in the past two weeks that have been blamed on Taliban elements fighting security forces along the border with Afghanistan.
A bomber blew himself up at the Marriott Hotel in Islamabad on January 26, killing a guard, while a suicide attack the next day in the northwestern city of Peshawar killed 14 people including six police officers.
Another bomber killed a policeman at a checkpoint in the tribal town of Dera Ismail Khan on January 29.
A suicide car bomber killed two soldiers in the remote town of Tank on Saturday.