The woman, 23, had requested weeks ago to be transferred from Nauru, part of Australia's offshore network housing people seeking asylum, to Australia so she could have an abortion.
Australia's top court is currently reviewing the legality of the centres.
Thousands of people joined protests at the weekend in support of refugees, and calling for the camps to be closed.
Meanwhile, Nauru has dismissed another Somali refugee's allegation she was raped.
The authorities said there was insufficient evidence to support the woman's claim she was raped by two Nauruan men.
Under Australia's tough asylum policy, any irregular migrants trying to reach the country by boat are intercepted and held in centres on Nauru and Manus Island, Papua New Guinea.
The government says this deters people-traffickers but there has been been criticism of the conditions at the camps.
In September, a report by the senate committee found conditions on Nauru were not "appropriate or safe". It said allegations of rape and abuse should be investigated.
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The 23-year-old Somali woman is reportedly more than 12 weeks pregnant. She alleges she was raped in the Nauruan community.
Abortion is illegal in the tiny island nation of Nauru, except where the mother's life is at risk. Rape is not considered a justifiable reason to seek a termination.
The Australian government had been under pressure to allow the women to enter the country for medical treatment.
"Our client is relieved that there has been a resolution to this sensitive matter," her lawyer George Newhouse told the Sydney Morning Herald.
"She is now in Australia and the Commonwealth government has agreed to provide her with medical treatment," he said, without giving further details.
Mr Newhouse said his client was grateful to "concerned Australians for their support" and to officials for their "understanding".
But an opposition politician has hit out at the woman's treatment.
"You've got to wonder why a young woman's very distressing situation had to become so public and the [prime] minister had to be pleaded with by the Australian people," said Greens senator Sarah Hanson-Young, AAP reported.
A Somali woman who became pregnant after allegedly being raped on Nauru has arrived in Australia.