The BBC said Father Denis "Chrysostom" Alexander had been remanded in custody in Sydney pending his extradition back to Scotland to face trial.
He is one of several monks accused of abusing boys at the former Fort Augustus Abbey boarding school in the Highlands.
The Crown Office declined to comment.
Father Alexander has always denied the allegations.
In 2013, he was confronted by BBC Scotland in Sydney as part of a documentary which led to a police investigation.
He is expected to face a further hearing on Wednesday at the local court in New South Wales, where it will emerge if he will oppose the extradition or not.