The woman, named by refugee advocates as Hodan Yasin, is currently in a critical condition, according to Australian Immigration Minister Peter Dutton. She has been transferred to Australia for medical treatment.
On Sunday, another refugee, named as Omid, died in an Australian hospital after setting himself alight on Nauru two days earlier in the presence of United Nations officials.
Critics say the self-immolations reflect the desperation of refugees living under Australia's controversial immigration policy.
Asylum seekers who arrive on Australian shores by boat are told they will never settle in the country, and are transferred to remote processing centers on the pacific islands on Nauru and Papua New Guinea.
Hundreds of people, including children, have lived for months or even years in these detention centers.
