The incident took place late Tuesday as the Pakistan International Airlines (PIA) flight arrived in Peshawar from Riyadh in Saudi Arabia with more than 170 passengers on board, airline spokesman Mashud Tajwar said.
"The shots were fired from outside the airport, one lady passenger and two stewards were wounded, the woman later died in the hospital," Tajwar told AFP, adding that the aeroplane landed safely.
Flights at the Bacha Khan International Airport in Peshawar have been temporarily halted following the gunfire, police said.
Muhammad Faisal, a senior police official, said that four to five bullets hit the aeroplane.
"Flight operations have been temporarily suspended," Faisal told AFP.
The attack comes after the Pakistan military launched a major offensive on June 16 in the most dangerous tribal district of North Waziristan along the Afghan border, where Taliban and Al-Qaeda-linked militants had taken refuge.
Police cordoned off an area outside the airport after the attack and have launched a search for those responsible, Faisal said, adding that one air steward was in a critical condition.
Another senior police official said the incident could have been catastrophic, as the PIA plane was flying only 1,500 metres above ground level when it was attacked.
"Credit goes to the aeroplane pilot that he managed to land safely," Najeeb Ur Rehman said.
Separately, Ansar-ul-Mujahedin militant group, a faction of the Pakistani Taliban, threatened Tuesday to carry out more attacks after claiming responsibility for a car suicide bombing in North Waziristan which killed two soldiers and a civilian.
"It is beginning of our offensive and we will launch attacks against government and local tribesmen if they form an anti-Taliban force," militant group spokesman Abu Baseer told AFP via telephone from an unknown location.
Though officials have not blamed any group for the incident at Peshawar airport, Taliban militants last week warned international firms and airlines to wind up their business in Pakistan or face attacks in the wake of the military offensive.
There have been several past incidences of firings at the airport, which is a commercial hub and also serves as a Pakistan Air Force (PAF) base in Peshawar, located on the edge of the tribal belt.
Aside from multiple rocket and mortar firings, in December 2012 Taliban militants launched a deadly attack on the airport targeting fighter jets and gunship helicopters, killing five civilians and wounding 50 others.