Erfan Paridari, 11, fractured his arm on May 4 after falling off a bicycle and since then doctors on the island and the International Health and Medical Services have been dithering on his treatment.
His family claim they were notified on Wednesday he would receive surgery in India.
But Mr Dutton says there are no plans to send the boy to India because there are medical services available on Nauru.
The boy's mother told the ABC her son has been in constant pain ever since his accident and needed urgent surgery.
She earlier said the family would be sent to India to receive medical treatment, but that the timing of the trip was still yet to be confirmed.
Australia was asked to send a specialist medical team to Nauru to operate on the Paridari, with doctors familiar with his case fearing he could be left disabled if he didn't get urgent surgery.
The Nauru government intervened on Monday to ask the federal Australian government to send the medical team.
"Decisive action was taken the moment we were advised of this boy's situation, and we wish him a speedy recovery," Nauru health minister Valdon Dowiyogo said in a statement.
Refugee advocate Ian Rintoul has been in direct contact with the boy's mother and says the immigration department notified the family on Wednesday afternoon that they would be flown to India for the boy's surgery.
"Why India? It's just madness," he told AAP, adding that the department was organising travel documents for a trip that was twice as far as going to Australia.
