The visit to Parliament House came on the fourth day of the King and Queen’s tour.
They have so far faced only low-key protests from critics, who displayed a banner with the word “decolonise” at an event in Sydney.
As Ms Thorpe shouted, the King spoke quietly with Mr Albanese on the podium while security officials stopped Ms Thorpe from approaching any further and escorted her out of the Great Hall.
Tony Abbott, the former Australian prime minister, who attended the event, expressed his dismay at the protest.
“It’s unfortunate political exhibitionism, that’s all I’d say,” he told the Australian press after the event.
Another of the guests, Keith Payne, a Victoria Cross recipient, said: “I was absolutely amazed that she got through the door. That was uncalled for and un-Australian.”
Speaking before the reception, Ms Thorpe told journalists that she was planning an outburst, claiming: “I’m going to tell him he’s not my King. He’s not our King.
“All of the wealth that he has created for his family has been stolen. He should apologise for taking our land. We need a peace treaty.”
Outside the venue, the King and Queen received a warm welcome from crowds who had been waiting for hours to see them.