The birds had been placed in three bags inside the plane's luggage compartment in an apparent attempt to smuggle them out of the country.
Investigators are working on tracking down the bags' owner.
The saker falcon (Falco cherrug) is a rare species protected by international and Kazakh law.
Saker falcons are used for hunting by the elite in Persian Gulf states. The average price for such a bird on the Central Asian black market ranges between $10,000 and $15,000.
Illegal trafficking of saker falcons from Kazakhstan and Kyrgyzstan to Persian Gulf countries was frequent in the 1990s.
More on the saker falcon (Falco cherrug):