The attack took place on 8 January in retaliation for the US-launched drone strike in Baghdad that killed Qassem Soleimani, a commander in Iran’s Revolutionary Guard.
Captain Bill Urban, spokesman for the US Central Command, said: “While no US service members were killed in the Jan. 8 Iranian attack on Al Asad air base, several were treated for concussion symptoms from the blast and are still being assessed.”
He added some service members were taken to US facilities in Germany or Kuwait for “follow-on screening” as a cautionary measure and would return “when deemed fit for duty”, in his statement released on Thursday.
President Donald Trump said there were no attacks in an address to the nation in the morning following the attack.
He said: “We suffered no casualties, all of our soldiers are safe, and only minimal damage was sustained at our military bases.”
It has been reported that the US had advance knowledge that missiles had been launched, thanks to an early-warning defence system, but the extent of damage to the bases was not immediately known.
As many as 1,500 Americans were deployed at the Al-Asad air base deep in Iraq’a Anbar desert.
Iran’s Supreme Leader Ayatollah Ali Khamenei said in a sermon on Friday the missile strikes on US targets were “such a slap to a world power” and showed support by “the hand of God”.
Mr Khamenei also called Mr Trump a “clown” during his sermon, adding the US president had only pretended to care about Iranians and will “push a poisonous dagger” into their backs.
He renewed his call for US troops to leave Iraq and the wider Middle East and said: “Resistance must continue until the region is completely freed from the enemy’s tyranny.”
In his sermon, he also accused Iran's "enemies", a term usually used to refer to the US and its allies, of using the accidental downing of Ukraine International Airlines flight 752 to direct attention away from Soleimani's death.
It took days for Iranian forces to admit to the mistake, initially blaming it on technical failures, but the delay sparked protests across Iran.