The Australian Federal Police are investigating allegations of a hoax targeting the Government's new coronavirus app.

The allegations concern images of an apparently fraudulent message, shared on social media, that told the recipient the COVIDSafe app had alerted the Government they are more than 20km from their home, and were required to phone the Government.

Federal Health Minister Greg Hunt said anyone found to be part of a hoax would be punished.

"Any misuse of telecommunications for a hoax is illegal," Mr Hunt said.

"Anybody who is found responsible will be charged with a significant criminal offence."

He said people who choose to spread misinformation should be fearful of the consequences.

"Whoever it is, they should be afraid of the law, because they are conducting a hoax which is about a very serious public health matter," he said.

A statement from a Department of Health spokesperson said the app did not have the capabilities the hoax reports.

"The COVIDSafe App does not have any geolocation capability, it does not track your location, only the proximity of your phone to other people’s phones that have downloaded the app, and cannot monitor a person’s location at any time," the spokesperson said.

"The app does not register a person’s home address and it does not share or send any information with anyone, until authorised by the user, if they have been diagnosed with COVID-19, and then only to state and territory health officials involved in contact tracing."

The COVIDSafe app was released on Sunday evening to assist contact tracing for those who become infected with coronavirus.

Mr Hunt told reporters on Tuesday that 2.44 million people had downloaded the app so far.

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