Fiji's Tourism and Civil Aviation ministry confirmed police were investigating the incidents, which it said occurred in the early hours of New Year's Day in the Nadi nightclub area.
"These alleged incidents are regrettable," the ministry said in a statement on Thursday afternoon.
Acting police chief Juki Fong Chew said the crew members were alleged victims of theft and assault. (HANDOUT/FIJI POLICE FORCE)
"There were two separate alleged incidents, one being alleged theft and the other being alleged sexual assault, which affected two different crew members.
"A suspect known to police for the alleged sexual assault has been questioned. Investigation continues."
Three Virgin crew members have been confined to their hotel rooms near Nadi International Airport since the incidents, and the airline has sent support staff to Fiji.
The ministry said the crew members were in good health and should return home by the end of the week.
"The three crew members were also advised by their headquarters to remain within the hotel vicinity to ensure contactability and assist with police investigations," the ministry said.
Flight Attendants' Association of Australia federal secretary Teri O'Toole said it appeared the airline had acted very quickly and her union was ready to assist in any way.
However, she said the union had not received an official approach for assistance.
"I believe these crew were on what we would call an overnight, so they would get to Fiji, wait and (their) flight would leave the next day," she told AAP.
Ms O'Toole said there had been a lot of guesswork about what had happened and urged people not to speculate while respecting the crew's privacy during the police investigation.
"This is not a very common thing but it's not something that's never happened before either," she said.
"It's very disturbing for their friends and colleagues. Everyone is very concerned for their welfare."
The airline has confirmed an incident occurred but no further details have been provided.
Virgin staff have travelled to Nadi to provide support and family members of the affected crew are reportedly flying to Fiji.
The Department of Foreign Affairs and Trade was aware of the reports but unable to provide further comment, a spokesperson said.
The Australian government advises travellers to exercise normal safety precautions when travelling to Fiji - the lowest of four official risk ratings.
"Crime in Fiji includes robbery, theft, violent assault, sexual assault and home invasions," the Smart Traveller website states.
"Most crime is opportunistic. The highest risk is in urban areas and at night."
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
