The General Civil Aviation Authority of the UAE, the Middle East's biggest travel hub, said that as a result of the new US policy it was suspending all flights by Iranian airlines until further notice.
Iran's Tasnim news agency reported that flights had also been shut down to Oman, Georgia and Azerbaijan, and to the Iraqi capital Baghdad.
It said authorities were working to route flights to another Iraqi airport, in Najaf, a major Shi'ite Muslim religious pilgrimage site.
The United States had announced it would put sanctions on any global companies doing business with Iranian airlines after September 23, with the aim of grounding Iran's entire civil fleet worldwide.
Other countries in the Gulf region also appeared to have restricted flights.
Tehran's Imam Khomeini Airport listed scheduled arrivals and departures on Thursday to and from countries including Afghanistan, Armenia, China, Iraq, Pakistan, Tajikistan and Turkey.
But no flights appeared to be listed to or from the nearby Gulf states, with which Iran has long had some of its most important business and travel ties.
Iran has suggested that enforcement of a US-mandated air blockade would lead to potential escalation.
On Wednesday, a senior Iranian official threatened to make airports "unusable" in any regional country that abides by the US ban.
With the US-Israeli war against Iran largely stalemated for months on the battlefield, the US has announced a shift in tactics to extend the reach of its financial sanctions by targeting companies from third countries that do business with Iranian firms, a practice known as "secondary sanctions".
A flight ban, if sustained, could deepen Iran's isolation and worsen an economic crisis in the country, which is already facing a US blockade of its ports at sea.
"We are living in an open-air prison," a retired teacher in Tehran told Reuters by text message on condition her name not be used.
The war, which Trump launched alongside Israel in February as "Operation Epic Fury," has disrupted global energy supplies, killed thousands of people and pushed up oil prices.
