Ahmet Yasar, the businessman who posted the image, told the BBC it was taken within the last four weeks by a friend who works as an airline captain.
Mr Yasar said the falcons were flying to Jeddah in Saudi Arabia for what is thought to be a hunting trip.
"The picture was taken on board an Airbus flying from an unknown origin to Saudi Arabia," Mr Yasar told the BBC.
"It is quite common for airlines in the Middle East to transport birds for hunting purposes. In this case each falcon is estimated to be worth about $8,000 (Â£6,435)," the Turkey-based businessman said.
"The picture I posted has gone viral attracting interest from all over the world," he said. "It is thought the birds were to be used to hunt geese."
Mr Yasar said the airline captain who took the picture did not want to be named.
The popularity of hunting in the Middle East was clearly seen in December 2015, when gunmen kidnapped at least 27 Qatari hunters - including members of the ruling family - in a desert area of Iraq near the Saudi border.
Iraq - like Saudi Arabia - is one of several countries frequented by wealthy practitioners of the ancient sport of falconry as they search for prey that either does not exist in their own countries or which has been almost hunted to extinction there.
Their favoured prey is the Asian houbara bustard, akin to a small turkey, and to find it and other similar species, Gulf hunters often travel to Morocco, Iraq, Pakistan and Afghanistan.
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They take with them their prized falcons, typically peregrines, sakers and lanners, which are expertly trained to home in on their quarry at high speed.
Falconry was an important skill for Bedouin hunters in the harsh deserts of Arabia and Syria and has been around for thousands of years.
A photo of 80 birds of prey on board an airliner in the Middle East has gone viral after being posted on Reddit.