Pauline Hanson received tickets, but Malcolm Turnbull is not on the guest list for Donald Trump's inauguration in Washington.
The prime minister confirmed on Monday he hadn't received an invitation to the US presidential swearing-in on January 20.
He seemed to suggest that even if he did, he may not have gone.
"I am very busy here, as you can see, as prime minister of this country looking after the interests of hard-working Australian families," Mr Turnbull told reporters in Toowoomba.
The Department of Foreign Affairs said the US State Department had advised that - as in the past - foreign delegations would not be invited.
Instead, heads of state and governments will be represented by chiefs of diplomatic missions in Washington.
Joe Hockey, ambassador to the United States, will represent Australia.
Party leader Senator Hanson revealed the "gift" on Twitter.
"Would you believe it? ... what an honour!" she tweeted.
The Queensland senator later said she won't be able to make the trip due to work commitments.
"My duties to the people of Queensland & Australia come first."
But NSW One Nation senator Brian Burston will be there after the party received a special invitation.
The tickets were reportedly arranged through Darren Brady Nelson, who worked on the Trump campaign and is now One Nation's economic policy advisor.
Fellow senator Malcolm Roberts had been originally slated to go but was replaced by Senator Burston after being admitted to hospital for urgent treatment on a hernia.
Senator Hanson and her federal One Nation colleagues toasted Mr Trump's November election victory with champagne outside Parliament House in Canberra.
She saw similarities between herself and the Republican president-elect.
"Why I'm celebrating is that I can see that people ... around the world are saying, we've had enough of the establishment," she said at the time.
"I can see in Donald Trump a lot of me and what I stand for in Australia. I think it's great."
Officials expect up to 900,000 people to attend the ceremony in the US capital, with American federal politicians getting nearly 250,000 free tickets for seats to give away.
The event is also expected to attract many protests.
