The COVIDSafe app, which is voluntary, is designed to help health authorities trace people who may have come into contact with someone who has Covid-19.
By Tuesday midday local time, 2.44 million people had downloaded the app, exceeding expectations, Australian health minister Greg Hunt said at a televised news conference.
"Australians have embraced their part in actions to prevent the spread of coronavirus," he said.
The app, which uses Bluetooth signals to track when people are close to another app user, has raised privacy concerns.
On Tuesday, health officials slammed a hoax message circulating online that purported to come from COVIDSafe app, claiming to detect when a user has moved from their nominated location. "The COVIDsafe app has detected you are now +20km from your nominated home address," the message reads, according to CNN affiliate 7 News.
Health authorities said the app does not collect data on a user's location.
"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," a department of health spokesperson told 7 News.
On Tuesday, Hunt said that it would not be physically or legally possible for any other authorities or nations, such as the US, to access the app's data.
"We have locked this down so completely, so thoroughly with the biosecurity rule, with legislation that is coming, the only people who can access the data are the state and territory health officials," chief medical officer Brendan Murphy told 7 News.
To sign up, users need to provide their name, mobile number, postcode and select their age range.