The directive comes after Iran launched missile strikes on two Iraqi military bases hosting US personnel on Wednesday (8 January).
Carriers have also been told by the FAA to avoid flying over the Gulf of Oman and waters between Iran and Saudi Arabia.
The missile attacks represent Iran’s first major act of retribution after top Iranian general Qasem Soleimani was killed in a US airstrike on Friday (3 January).
There is no indication at this stage whether the strikes resulted in any casualties at the two Iraqi bases.
US president Donald Trump tweeted he would make a statement on Wednesday morning, adding: "all is well. Assessment of casualties and damages taking place now."
’Heightened military activities and increased political tensions’
The FAA said the directive came in response to "heightened military activities and increased political tensions in the Middle East, which present an inadvertent risk to US civil aviation operations”.
"The Federal Aviation Administration issued notices to airmen outlining flight restrictions that prohibit US civil aviation operators from operating in the airspace over Iraq, Iran, and the waters of the Persian Gulf and the Gulf of Oman," it said in a statement.
"The FAA will continue closely monitoring events in the Middle East. We continue coordinating with our national security partners and sharing information with US air carriers and foreign civil aviation authorities."
Iran’s missile strikes are not currently being connected to a crash involving a Ukrainian International Airlines passenger jet, which came down shortly after taking off from Tehran on Wednesday morning.
Foreign carriers typically mirror the FAA’s flight directives. Singapore Airlines and Qantas have already indicated their aircraft will steer clear of the zone as set out by the FAA.
Foreign secretary Dominic Raab said: "We condemn this attack on Iraqi military bases hosting coalition – including British – forces.
"We are concerned by reports of casualties and use of ballistic missiles.
"We urge Iran not to repeat these reckless and dangerous attacks, and instead to pursue urgent de-escalation.
"A war in the Middle East would only benefit Daesh [Isis] and other terrorist groups."
