The tournament, which also includes Australia, South Africa and New Zealand, has been operating under strict biosecurity protocols in Australia's northeastern state of Queensland due to COVID-19.
Sanzaar said the group had broken the tournament's rules when they travelled across the Queensland state border with New South Wales to visit Byron Bay, a popular tourist destination, on Wednesday.
"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 said in a statement.
"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 Argentina rugby union (UAR) said the players group comprised Pablo Matera, Sebastián Cancelliere, Joaquín Díaz Bonilla, Felipe Ezcurra, Santiago Medrano and Santiago Socino, the team manager's Lucas Chioccarelli and video analyst Rodrigo Martínez.
They were forced to stay at a hotel in New South Wales overnight after being turned back at the Queensland border by police for failing to produce required documentation.
Sanzaar said they would remain in the state until rejoining the rest of the Argentina squad on Sunday ahead of their departure from Australia.
"All are in perfect health, staying in a hotel in the area, waiting for their condition to be resolved," the UAR said, adding it was a "top priority" to bring the players back to the camp.
"In parallel, an internal process has begun to clarify what happened and determine the corresponding responsibilities."
The players will be unable to feature in Argentina's final Rugby Championship match against Australia on the Gold Coast on Saturday.
Argentina have lost all five matches they have played in the tournament.
