"There are no Taiwanese obstetricians and gynaecologists with experience in performing pregnancy terminations on women with FGM," Justice Alan Robertson said in his judgement on Friday.
The woman is approximately 12 weeks pregnant and has been on Nauru for almost five years.
The judgement said she has a history of mental illness, including a number of suicide attempts.
Obstetrics and gynaecology professor Caroline de Costa gave evidence that hospitals in Sydney and Melbourne now have "considerable experience" in dealing with such cases.
In making his ruling, Justice Robertson said that infibulation - or the practice of removing parts of female genitalia - carries "significant emotional and psychological implications and those aspects of care need to be expertly managed".
He said there would be "substantial risks in performing the termination in other environments or by practitioners without the relevant experience [including] immediate physical risks ... and major psychological trauma and post-traumatic stress disorder".
The Refugee Action Coalition says that 1,600 refugees remain on Nauru and Manus.
The offshore policy is designed to deter people embarking on treacherous sea journeys, but the United Nations and other rights groups have criticised the camps' conditions and long detention periods.