Khan, who was at the site of the crash, said witnesses told him "the aircraft has crashed in a mountainous area, and before it hit the ground it was on fire".
Images shown on Pakistani TV channels and circulated on social media showed a trail of wreckage engulfed in flames on a mountain slope.
Irfan Elahi, the government's Aviation Secretary, told media the plane suffered engine problems but it was too early to determine the cause of the accident.
PIA said the plane was carrying 48 passengers, including five crew members and a ground engineer. But Sohail Ahmed, a PIA official in Chitral, said there were 41 people on board, while the Civil Aviation Authority (CAA) earlier put the number of people on board at 47.
A local trader at the site of the crash said the fire was still burning nearly two hours after the crash, with rescue officials now on the site.
"They are removing body parts," trader Nasim Gohar told Geo TV.
The military said it had sent troops and helicopters to the site of the crash.
A PIA spokesman said the dual turboprop engine plane lost contact with the CAA at around 4:30pm (1130 GMT).
"PIA is doing everything possible to help the families of passengers and crew members," the airline said in a statement.
According to the flight manifest, there were three people on board with foreign names.
Plane crashes are not uncommon in Pakistan and safety standards are often criticised.
In recent years, media have reported on multiple near-misses as planes over-ran runways and engines caught fire.
In 2010, a passenger plane crashed in heavy rain near Islamabad, killing all 152 people on board. Two years later, a plane operated by a private Pakistani company, with 127 people on board, crashed near Islamabad. All on board were killed.
PIA has also suffered major disasters in the past.
In 1979 and 1992, PIA jets crashed in Jeddah, Saudi Arabia and Kathmandu, killing 156 and 167 people, respectively.
In 2006, a PIA plane crashed near the central city of Multan killing 45 people.