He was later transferred from Christmas Island to Papua New Guinea.
He has a long history of infringements during his time in detention, including throwing boiling water on a guard and punching a security officer who confiscated his pornography.
Currently in detention in Queensland, he will receive treatment at a private hospital on the Gold Coast.
Genital reconstructive surgery can cost up to $10,000, reports Daily Mail Australia.
Home Affairs Minister Peter Dutton, who approved the transfer, has previously said that his powers to block such transfers have been dramatically cut.
The case has generated fierce debate across the Tasman, with politicians from both sides of the house weighing in.
National MP Barnaby Joyce told the Sunrise show: "This individual had a pretty chequered past, he'd been up for assault against one of the guards.
"He's been creating real problems and this brings into focus the Medevac laws and why we'd be bringing this person to Australia."
Labor's Joel Fitzgibbon said: "Medevac laws have made no change to this situation.
"Peter Dutton would have brought this person to Australia pre-Medevac laws because despite the ridiculous nature of the events that lead to it, he would have always been brought here if he self-harmed and faced such serious injuries."