Australian health minister Greg Hunt's mobile phone was hacked this week in an attempt to find contact information for Hong Kong activists, the second government official to report a breach this week.

"A cyber security attempt to impersonate the minister has been referred to the Australian Federal Police (AFP) and investigations are underway," a statement issued by Hunt's office on Thursday said.

Australia's finance minister Simon Birmingham issued a similar notification to authorities on Monday after he was impersonated on the social messaging Telegram app asking people "do you have any contacts in Hong Kong?"

Some people responded with contact details of Hong Kong residents, according to national newspaper The Australian, believing that they were engaged in a conversation with Birmingham.

"The AFP are seeking, through data security processes, to attempt to ascertain how any data was secured and are working to try to get Telegram to shut down the false account," the finance minister said in a parliamentary hearing Tuesday.

Authorities were first alerted to the hacking campaign on March 18 and issued a statement at the weekend explaining how the scam messages lure recipients to share personal information.

"It appears to be in the form of a message from an associate and encourages recipients to download a messaging app for further communications," the AFP said.

The full extent of the hack remains to be seen, with some people also receiving bogus requests for money from the ministers to be sent to a bank account outside Australia.

Australian Prime Minister Scott Morrison's office declined requests by local media to comment on the ongoing investigation.

The head of Australia's Liberal Party is otherwise occupied with accusations of fostering a culture of misogyny and prejudice in the seat of national government, where it recently emerged a young staffer was raped in a minister's office two years ago.