An Iraqi government order that worldwide airlines halt all flights in and out of the cities of Erbil and Sulaimaniyah in Kurdish territory is set to kick in on Friday.
"We have an global community here, so this is not going to be only against Kurdish people", Irbil airport's director, Talar Faiq Salih, told the BBC on Thursday.
Masoud Barzani's KRG says Monday's referendum, which delivered an overwhelming yes for independence, was meant to pave the way for a peaceful secession from Iraq, through talks with Baghdad and neighboring states Turkey and Iran.
Ankara has repeatedly threatened a series of measures to isolate the Iraqi Kurds including shutting the border and halting its transit of oil from the KRG to the Turkish Mediterranean port of Ceyhan, an economic lifeline for the Iraqi Kurds. As they aspire to statehood, could the Iraqi Kurds-as Haider al-Abadi, the prime minister in Baghdad, has threatened to ensure-now lose everything?
Turkish President Recep Tayyip Erdogan says Iraq's Kurdish region has "thrown itself into the fire" by holding a referendum on independence from Iraq.
Flights to Erbil and Sulaimaniya operated by domestic operators will be allowed to continue, the CAA's Mohsen said. The referendum for independence was exclusively for Iraqi Kurdistan, already a semi-autonomous region.
"We were supposed to go back to Brazil next Saturday but we rescheduled our flight", said Isidoro Junior, a 32-year-old volunteer for an NGO providing medical assistance to Iraqis displaced by the war against IS.
Over the past three days, there has been an exodus of foreigners from Kurdistan who fear they won't be able to leave after Friday.
"The halt on worldwide flights is now officially into effect", Mawloud Bawa Murad, the Kurdish regional government's transport minister, told AFP at Arbil airport, where he was visiting staff.
In defiance of Baghdad, the self-ruled Kurdish region has been unilaterally exporting crude oil produced in their region and contested areas through Turkey.
In a statement read in the Shiite holy city of Karbala by cleric Ahmad al-Safi during Friday prayers, al-Sistani said all parties in Iraq should abide by the Iraqi constitution.
The decision came hours after the Kurdistan administration announced that 92.73 per cent of the 4 million people who took part in Monday's referendum on independence from Iraq voted "yes".
As IS's self-styled caliphate crumbles, the question of what comes after it hangs over the Middle East. Mr Barzani has acted to prevent a return to the status quo ante, in which there was no Kurdish state.
An Iraqi government order that worldwide airlines halt all flights in and out of the cities of Irbil and Sulaimaniyah will kick in Friday evening local time.
Defense Secretary Robert Gates arrives at Irbil International Airport in Irbil, Iraq.
Turkey has many reasons to block Kurdish independence efforts, of course. The idea of an independent state has been central to Kurdish politics for decades.