Prime Minister Anthony Albanese said an Iranian strike landed near the base at Al Minhad in the United Arab Emirates just after 9am on Wednesday (AEDT).
Mr Albanese said no Australian troops were wounded and that "everyone is absolutely safe at this point in time".
"We recognise that the Iranian regime is continuing to engage in frankly random attacks right across the Gulf region," he told reporters in Tasmania on Thursday.
An accommodation block and a medical facility were damaged by a small fire caused by the missile hitting the road leading up to the base.
Australia has sent a Royal Australian Air Force E-7A Wedgetail plane to the Middle East.
Earlier, Donald Trump declared the US doesn't need the help of its allies who rejected his calls to help to take back a major oil-shipping corridor.
In a scathing statement posted to his social media platform Truth Social, the US president blasted Australia and other Indo-Pacific nations for their refusal to get involved in the conflict with Iran.
"The United States has been informed by most of our NATO 'Allies' that they don't want to get involved with our Military Operation against the Terrorist Regime of Iran, in the Middle East," Mr Trump's post said.
"We no longer 'need' or desire, the NATO Countries' assistance — WE NEVER DID! Likewise, Japan, Australia, or South Korea."
The conflict, triggered by US-Israeli strikes on Iran, has sent fuel prices skyrocketing globally after the de-facto closure of the Strait of Hormuz due to Tehran's retaliatory actions.
The US president had requested a naval coalition to help secure the key shipping route, through which about a fifth of the world's oil supplies travels.
But Treasurer Jim Chalmers deflected Mr Trump's criticism, saying Australia's government had not considered sending any vessels to protect oil tankers in the strait.
Labor has previously said Australia had not received a formal request from the US to provide a warship.
Opposition frontbencher Andrew Hastie took aim at Mr Trump's post.
"It was a petulant post from a president under immense pressure ... relationships that are longstanding, you show respect and I don't think it was a respectful post at all," he told ABC radio.
"We've got a proud history and I just don't think that's how you treat allies. It's a reflection on his character more than us."
Mr Albanese said he would continue to engage diplomatically with the US president.
Israel's ambassador to Australia Hillel Newman said his country wanted the war to be as "short as possible" and said the Iranian people were being crushed under the current regime.
"We have no deadline," he told reporters in Canberra.
"It's a matter of attaining the objectives. Once we attain the objectives, the war will be over."
Former Liberal prime minister Malcolm Turnbull said Mr Trump was "lashing out".
"He's furious that America's allies are not prepared to support him in a war that he started without their consent or ... without any consultation," he said.
"It really just underlines ... the importance of Australia being more independent, exercising our own sovereignty."
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