It's believed someone breached the security surrounding Medicare details, potentially exposing Australians to fraud.
Federal police are now investigating the "traditional criminal activity", which was revealed on Tuesday.
A report on 'The Guardian Online' website detailed how one of its own reporters was able to buy his Medicare card number from a darknet trader for less than $30.
Human Services Minister Alan Tudge declined to elaborate on the "most likely problem", but cited previous cases of doctors' surgeries being broken into.
"I have my strong suspicions but we're leaving it obviously up to the police to do a proper investigation," he told ABC radio on Wednesday.
He again admitted the government wasn't aware Medicare details were being sold on the dark web until the report.
But he insisted personal health records aren't at risk and those saying otherwise were indulging in fear-mongering and being irresponsible.
"Someone hasn't hacked into a database," Mr Tudge said.
"There is no indication this is widespread."
At least 75 files are believed to have been sold since October last year.
However, Mr Tudge couldn't confirm this, saying only that the government believed the number of those affected was a "small number in the dozens".
"The people that we know had a Medicare card number breach, we have contacted," he said.
Doctors are seeking government assurances that patient records are secure.
"This is a deeply concerning," Australian Medical Association president Michael Gannon said.
The AMA fears the Medicare issue might dissuade Australians from taking part in the government's 'My Health Record' online patient health information program.
"It is so important for the success of the My Health Record that doctors and patients both have absolute confidence in the integrity of the system," Dr Gannon said.
Mr Tudge later told Sky News he had given the AMA president a confidential briefing.
