The order comes as tensions mount between Washington and Tehran after Iran shot down a US surveillance drone on Thursday (20 June). This followed a series of incidents in the Gulf region, including strikes on oil tankers.
United Airlines pulled flights between Newark and Mumbai, which currently overfly Iran, hours before the FAA made the order.
Iran said the drone strayed into its airspace, but the US has denied this.
The FAA said flights were not permitted in the overwater area of the Tehran flight information region until further notice “due to heightened military activities and increased political tensions that might place commercial flights at risk”.