The 59-year-old, known as Father F, was arrested at a home in Armidale in northern NSW, and faced court in the afternoon in relation to the charges dating back to the 1970s and '80s.
The Herald Sun reports that he faces up to 10 years in jail if found guilty of the offences.
Magistrate Mark Richardson denied his bail application and ordered the man's name not be published to protect the anonymity of the alleged victims.
The SMH reports that following his arrest, police urged anyone with information about an alleged cover-up by the Catholic Church to come forward.
"It's certainly early days in regards to our investigation in respect to the alleged cover-up that's been suggested," Detective Superintendent Kerlatec said.
The offences were allegedly discovered after police formed Strike Force Glenroe in July.
Detectives have spoken to 50 people, including potential victims, their families and others who may have information.
The police say the victims were were all young girls aged between five and 18 when they were allegedly sexually and indecently assaulted by the former priest.
The Bishop of Armidale, Michael Kennedy, released a statement saying he was not able to comment on the matter.
"I again take this opportunity to extend my deepest sympathy to victims of child abuse and their families, and reassure the community of my commitment to see justice achieved."