The tournament has been held under strict biosecurity protocols with restricted travel because of Covid-19 cases in the state of Queensland.
But the players crossed into New South Wales to visit the tourist destination.
The group included former Pumas captain Pablo Matera.
The Argentina rugby union (UAR) said the group also comprised Sebastian Cancelliere, Joaquin Diaz Bonilla, Felipe Ezcurra, Santiago Medrano and Santiago Socino, the team manager Lucas Chioccarelli and video analyst Rodrigo Martinez.
The group had to stay in a hotel in NSW on Wednesday night after being stopped at the state border by police for failing to produce the required documentation.
Sanzaar, the governing body that oversees the Rugby Championship, said: "Sanzaar has informed Argentina Rugby that all members of this group are now ineligible to participate further in The Rugby Championship as they have breached tournament rules.
"Sanzaar is very disappointed that such a breach has occurred given the clear rules that are in place to ensure the health and safety of all players and staff, and compliance with all relevant health orders."
The six players will be unable to play in Argentina's final Rugby Championship match against Australia on Saturday, and will remain in NSW until the team's departure from the country on Sunday.
The Pumas are yet to win a game in this year's tournament.
The players' expulsion comes days after Sanzaar and Rugby Australia apologised to Argentina after the they were left out of a team captains' photo shoot.
Meanwhile, Australia head coach Dave Rennie has named 38-year-old prop Greg Holmes on the bench for his first game since 2016, and back-rower Sean McMahon for his first since 2017 for Saturday's match.
Holmes, who will become the oldest Wallaby since World War Two, joined up with the squad in August to help out younger players.
He had initially met with Rennie for a beer in Perth only to ask if he could come into camp to take notes for when he moves into coaching, but Rennie later asked him to join up as a player.