Pakistan's army rushed reinforcements to the scene of the night attack, one of the most audacious raids by militants since an assault on an air base in the east of the country in August.
All the five attackers were shot dead by forces while an explosive-laden was also seized, ISPR said.
According to sources, one of the attackers was arrested in injured condition as search operation continued.
According to health officials, more than 40 had been wounded at the airport, which handles civilian and military traffic.
Pakistan's air force said a rocket attack had damaged the outer wall of the air field, which lies near a residential area and military barracks in Peshawar.
"No terrorist has been able to penetrate inside (the air field)," Group Captain Tariq Mahmood, a spokesman for the Pakistan Air Force, said in a statement. "Security forces were fully alert and are in control of the situation."
Mahmood added there had been no casualties among the Pakistan Air Force or damage to equipment during the incident.
Three rockets also hit a nearby residential area, a military official said.
"We have repulsed the attack on the airport, everything is now under control," the military official added.
Hospital staff scrambled to treat wounded brought from the scene of the attack, where residents described hearing gunfire and explosions.
"An emergency has been declared in the hospital and all the surgeons have been called," said Umar Ayub, chief executive of the Khyber Teaching Hospital Peshawar. "All of them suffered bullet injuries and some of the injured are in critical condition."
Peshawar has witnessed many bomb attacks and shootings in recent years, but residents said it was the first time such a large attack had been staged on the airport.
There was no immediate claim of responsibility.
Presidentdirected Khyber Pakhtunkhwa Governor Masood Kausar to submit a report into this attack.
Prime Minister Raja Pervaiz Ashraf contacted Chief Minister Amir Haider Hoti and sought details of the attack.