The young African refugee, known in court documents lodged with the Federal Court of Australia as S99, was reportedly raped while suffering from an epileptic seizure while staying on Nauru as a resettled refugee.
According to Fairfax, she is now nine weeks pregnant and is seeking an abortion on mainland Australia.
The woman is not believed to have received any ongoing psychological care and has reportedly attempted suicide.
Abortion is illegal on Nauru, and last week Australian authorities reportedly transferred her to Papua New Guinea where abortion is a criminal offence.
Under PNG law, abortion is only legal if the mother's mental or physical health are at stake.
According to Fairfax, the woman has filed a document with the Federal Court through her lawyer requesting an abortion on Australian soil.
In the document she says "I am very concerned about having it in PNG, because I am scared about the level of care because of my epilepsy... and because I could go to jail if it isn't legal; I want to have a termination in a safe place."
Stephen Donaghue, QC, who is representing the Department of Immigration told the Federal Court that Australia is not responsible for the woman's welfare.
"She's not in any way, in our submission, under the control of the Commonwealth in the way that an immigration detainee traditionally should be.
"Having gone to PNG, she's not detained by the Commonwealth," he told Fairfax.
Barrister Julian Burnside told SBS he was extremely concerned by the situation.
"It's horrifying that Australia has essentially taken control of her life. She arrived in Christmas Island, we forcibly removed her to Nauru. She's been raped, she wants an abortion but can't have it on Nauru, and asks to be sent to Australia. I think it's outrageous.
"And frankly, the government's position that Australia is really not in control of her life is really completely absurd," he said.
