The duo were questioned by Brisbane police on Friday in relation to an assault that left a taxi driver in a critical condition in hospital.
While the ARU bucked expections of an alcohol ban for all players at the World Cup, a meeting between the team hierarchy decided to impose a midnight curfew for the tournament and at all related training camps prior to the event in France.
Australian Rugby Union chief John O'Neill, head coach John Connolly, captain Stirling Mortlock, team manager Phil Thomson, assistant team manager Chris Webb, ARU head of legal Nick Weeks and ARU general manager of the high performance unit Pat Howard headed the meeting and made it clear to Tuqiri and Dunning of the standards required of them in the national team.
O'Neill said: "The ARU has made it abundantly clear to both players how disappointed we are that they put themselves in harm's way and that the warning they have been issued should not be taken lightly.
"Being a Wallaby is an honour, not a right. These individuals are looked up to by the community and there are high standards they are expected to meet.
"Exposing themselves, the team and the game to intense and unnecessary scrutiny and criticism clearly does not meet these standards.
"We have told the players in no uncertain terms that this is a very serious warning they have been issued and that they should be very mindful of their conduct in the future, as a repeat of this behaviour will not be tolerated.
"I expect today's meeting and the subsequent warning will serve as a strong reminder of their responsibilities."
While an alcohol ban has not been imposed, O'Neill made it clear to Tuqiri and Dunning that good judgement and discretion should be imposed while drinking.