Immigration Minister Peter Dutton has denied claims a child detained on Nauru is to be taken to India for treatment for a broken arm.

But the 11-year-old's mother has twice told the ABC she was told otherwise.

Erfan Paridari's mother said her son broke his arm about a month ago after falling off a bike.

He received treatment at the local hospital, but staff there did not set the bones in his arm properly.

"My case worker yesterday called me and says I am wait [sic] for document because they need to make it for me and my family document, travel document," she said this morning via telephone.

"And after that they send all my family in India for assessment."

The boy is living on Nauru with his mother, father and sister.

His mother said the boy had been in constant pain and needed urgent surgery or he risked permanent disability.

When asked to confirm the plan was to send the family to India, and travel documents were being organised, the mother said: "Yes."

But Mr Dutton says there is no such move afoot.

"It's not true and we have medical services that are available in Nauru and the Nauruan government obviously has the system up there to provide people with support that need it when it comes to medical attention," he told Macquarie Radio.

"We will provide support otherwise, but the story about going to India is not true."

Nauru's government has told the ABC an Australian medical team is being sent to the island nation to treat the boy.

Earlier, the Refugee Action Coalition's Ian Rintoul — who was also in contact with the family — said the lack of detail was worrying.

"They just got a bare message that they'll have to wait for the travel documents to India," Mr Rintoul said.

"It doesn't really settle any of the immediate questions — why there should be a continued delay to go to India, what kind of treatment they're actually going to get in India, where they're going to be treated, what arrangements are being made for post-operative care and rehabilitation."

Greens senator Sarah Hanson-Young said if the claims were true, it was incomprehensible.

"You couldn't make this stuff up, what on earth is going on?" Senator Hanson-Young said

"This is a family who are found to be refugees, they are genuine refugees, they've been dumped on Nauru by this Government, the boy needs medical assistance — just bring him to Australia and let him be relieved from the suffering of a broken arm."

Senator Hanson-Young said Australian taxpayers would be left to foot the bill if the transfer went ahead.

"You've got to wonder how much it's costing the Australian taxpayer, because of course the deal that Australia has with Nauru is that all costs of those that are found to be genuine refugees left on Nauru, the Australian Government has to foot the bill," she said.

"I've never heard of this happening before."