Officials say the aircraft suffered engine problems soon after take off from the mountainous region of Chitral last Wednesday, but it is not clear what caused the crash about 50 km from the capital, Islamabad, its destination.
"Yes, the chairman of PIA has resigned due to personal reasons," Danyal Gilani, spokesman for PIA, told Reuters.
Citing sources, Pakistani English-language newspaper The News, said Saigol had come under pressure to resign in the wake of the crash.
The media focus in Pakistan following the crash has fallen on PIA's safety record, but the loss-making state carrier has vehemently denied media reports that there was a fault with the aircraft before the takeoff.
On Monday, PIA grounded its fleet of 10 European-made ATR planes after Pakistan's Civil Aviation Authority decided to conduct "shakedown tests" of the carrier's entire ATR fleet.
Officials say the crashed ATR-42 aircraft, built in 2007, had racked up 18,739 flight hours since joining PIA's fleet that year and the plane's captain, Saleh Janjua, had logged more than 12,000 flight hours over his career.