The notice posted on the X platform said the move is to ensure the safety of residents and visitors.
The shutdown of Qatari airspace comes as Iran repeated earlier threats to retaliate against the United States after strikes on its nuclear sites.
Qatar hosts Al-Udeid Air Base, the largest US base in the Middle East, which serves as the forward headquarters for US Central Command and accommodates approximately 10,000 troops.
The US embassy in Qatar emailed US citizens in the country on Monday recommending that they shelter in place until further notice, triggering a slew of messages from various Doha-based institutions to employees and students.
The United Kingdom government later issued a warning recommending the same for UK citizens in Qatar.
The US and UK messages noted that the recommendation was "out of an abundance of caution" and offered no further information.
Two US officials separately told Reuters that Iran could carry out attacks targeting US forces in the Middle East soon, with one source saying it could happen in the next day or two.
Commenting on the message, Qatari foreign ministry spokesman Majed al-Ansari said in a statement that the security situation in the country remained stable, adding that the embassy's advisory did not suggest any specific threat.
Al-Ansari said Qatar was ready to take all necessary measures to ensure the safety of its citizens and residents.
There was confusion among residents in Qatar over how to react to the mixed messages coming from the Qatari and embassy authorities on Monday afternoon.
The Qatar campuses of US universities offered differing advice to their staff and students, with Texas A&M University saying an evacuation of their building had been ordered, Northwestern University requesting that people go home and Georgetown University telling people they could go home if they wished.
Israel struck the most notorious jail for political prisoners in Tehran on Monday in a potent demonstration that it was expanding its targets beyond military and nuclear sites.
Ebrahim Zolfaqari, a spokesman for Iran's Khatam al-Anbiya central military headquarters, issued an apparent threat to retaliate after US President Donald Trump approved attacks on Iranian nuclear sites at Fordow, Natanz and Isfahan.
"Mr Trump, the gambler, you may start this war but we will be the ones to end it," Zolfaqari said on Monday in an English-language video statement.
Iranian authorities have repeated earlier threats to retaliate against the United States but it had yet to do so in a meaningful way more than 24 hours after US bombers dropped 30,000-pound bunker-busters on Iran's underground nuclear sites.
Trump's administration maintains that its aim is solely to destroy Iran's nuclear program, not to open a wider war.
The US administration says it is still seeking a diplomatic resolution that would have Iran forgo any reprisal.
with AP and PA
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