Mahmood was famed for taking 12 wickets at the Oval ground in London in Pakistan's first year in Test cricket in the 1954, as well as in the country's two inaugural wins at Lucknow, India.
"Mahmood suffered a heart attack which he couldn't survive. He was otherwise healthy and used to go to his office even after a prostate operation," his son Shahazad Mahmood told AFP.
Mahmood, also a police officer, played 34 Tests, taking 139 wickets and also led Pakistan in 10 Test matches between 1952 and 1962.
Before the partition of India and Pakistan Mahmood played in the Ranji Trophy for Northern India and although selected for India's tour to Australia in 1946 he chose to migrate to Pakistan and sought a career in the newly formed country.
He was remembered for his devastating leg cutters as a medium pacer, often unplayable on the matting picthes used on the sub-continent before grass turf pitches were introduced.
He took 12 for 99 at the Oval on Pakistan's 1954 tour, highlighted by the British media which reported: "England Fazal-ed."
Mahmood also played a lead role in Pakistan's first ever win over Australia, taking 13 for 114 at Karachi in 1955.