"Tens of surface-to-surface missiles," were fired at the strategic airbase and the attack was also confirmed by the White House and Pentagon, reports the Tehran-based Press TV.
The attack comes after the IRGC had called for a complete withdrawal of US troops from the Iran, asserting that it would not differentiate between the Washington and Israel while retaliating against Soleimani's killing.
"We warn US allies providing bases for the (American) terrorist army that any country serving as the origin of bellicose and aggressive attacks in any form against the Islamic Republic of Iran will be targeted," the IRGC said in a statement on Wednesday.
It urged the US to recall all their soldiers back home to prevent more damage.
Meanwhile, the semi-official FARS News Agency in a report said that a second wave of surface-to-surface missiles on Wednesday hit the two US airbases of Ain al-Asad and Harir Camp.
Fars News Agency reported that the missiles were probably of Fateh 313 type and they were launched from Iran's western Kermanshah Province.
Fateh 313 missiles are road-mobile single-stage solid-fuelled surface-to-surface missile with a range of 500 km.
The Pentagon in a statement confirmed the missile attack, saying "Iran launched more than a dozen ballistic missiles against US military and coalition forces in Iraq".
It further said that it would take all necessary measures to protect and defend US personnel, partners, and allies in the region.
The White House said earlier that it was monitoring the attacks, adding that President Donald Trump was also following the situation closely and consulting with his national security team.
"We are aware of the reports of attacks on US facilities in Iraq," Efe news quoted White House press secretary Stephanie Grisham as saying on Tuesday night.
"The President has been briefed and is monitoring the situation closely and consulting with his national security team."
In response to the attack, Trump tweeted: "All is well. Missiles launched from Iran at two military bases located in Iraq. Assessment of casualties and damages taking place now...
"We have the most powerful and well equipped military anywhere in the world, by far. I will be making a statement tomorrow (Wednesday) morning."
The strikes came hours after Trump's latest warning to Iran earlier on Tuesday.
"If Iran does anything that they shouldn't be doing, they're going to be suffering the consequences, and very strongly," Trump told reporters in the White House.
Trump's remark came after the IRGC Commander Hossein Salami warned the US also on Tuesday that Tehran would take "severe revenge" over the death of Soleimani, who was the chief of the elite Quds Force.
( With inputs from IANS )