Police initially thought he was a suicide bomber, but later discovered the man had failed to throw the grenade and died in the attempt.
Police said one policeman was wounded by gun fire. The other wounded security man was hurt in the blast.
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.
Suicide attacks
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.