Seven detainees at the Christmas Island Detention Centre are being transferred to a facility in Perth.
There are unconfirmed reports that all seven are New Zealand citizens.
A statement from the Australian Minister for Immigration and Border Protection Peter Dutton says the detainees are "travelling on a charter flight accompanied by security officers".
"Restraints are used where appropriate for the safety and security of detainees, staff and the aircraft."
Macquarie Radio in Sydney has been told they are part of the group that caused major damage to property over two nights.
The repair bill is expected to cost more than $1 million.
Investigations into the damage are continuing.