Grand Ayatollah Ali al-Sistani says such acts are against the "religious laws and the moral principles of Iraqis and affect the reputation of the country."
The top cleric also described the abductors as "criminal gangs" and called for the release of the Qataris.
Al-Sistani's comments were relayed through his representative, Ahmed al-Safi, during the Friday prayers' sermon in the holy city of Karbala.
Hunters from Gulf states, mainly Qatar, often visit Iraq's vast western and southern desert areas to hunt and purchase falcons. Iraqi authorities approve the expeditions and provide protective forces that accompany the hunters.