It took five hours for Australians to download the COVIDSafe app at a rate the government expected would take five days, the ABC reports.
The app was released at 6:00pm on Sunday and by 10:30pm 1 million Australians had downloaded it.
"At 6:00am, it was 1.13 million Australians who had downloaded the app," Health Minister Greg Hunt said on Monday morning.
"We got the first million within five hours. We had been hoping, our best hope, was we might get to 1 million in five days."
Downloading the app is voluntary but the government has previously said 40 percent of Australians - or 10 million people - need to take up the contact-tracing app for it to be a success.
Health, business and union leaders joined forces on Sunday to call on Australians to download the app.
And politicians across the political spectrum have offered their support, with many taking to social media to post screenshots of the downloaded app.
Queensland Premier Annastacia Palaszczuk said she had not downloaded it but planned to do so later today.
The state's Health Minister Steven Miles told the ABC he was also yet to download the app and would seek his own "advice" to assure himself of its safety.
"I've heard those assurances from the Federal Government so I'm sure all of those measures are in place," he said.
"But I think Queenslanders would want me to be able to tell them that I really was confident in those things so I want to take some time to have a look at it."
Digital rights advocates have called for the source code to be made public so the inner workings of the app can be scrutinised.
Mr Hunt said Australia would follow other countries such as Singapore in making that code public.
"The source code will be released within two weeks," he said.
"The reason for that is that there's a constant review of the safety and security.
"Our first task is to make sure the security assessment is done and that there is absolute protection of privacy above all else."
Labor's health spokesman Chris Bowen, who has downloaded the app, said he accepted the government's decision on the coding.
"I'm prepared to take the government on good faith on that if that's what they're working through," he said.
"Of course it should be released, but if they need a little bit of time to sort that through and work out how much should be released then I'm prepared to give them that."
However, questions remain about the technology's performance on iPhones.
COVIDSafe uses Bluetooth to record anonymised IDs from users who are within 1.5 metres of each other for about 15 minutes.
It aims to identify those exposed to Covid-19 once someone is diagnosed.
Those with Android smartphones can use their devices normally while the app runs in the background.
However, if an iPhone is in low-power mode, it may affect the ability to track contacts, according to a spokesperson for Government Services Minister Stuart Robert.
It has also been suggested the iPhone app may not work effectively if too many other Bluetooth apps are running.
Use of the app has been encouraged by Hunt and Prime Minister Scott Morrison, who have both said it will be a vital tool in helping Australia ease restrictions designed to stop the spread of coronavirus.
"It assists in the early alert and finding of people who may have been in contact with a person who is positive with a diagnosis," Hunt said.
Mr Morrison moved to allay privacy concerns on Sunday, saying only health officers would have access to the data the app collected.
"It's another tool we need to get back to normal as much as we can," he said.
"No other government agency can use this information, no-one in the Commonwealth Government at all. And in state authorities, only the health officer can use it.
"Not the police, not the welfare people, nowhere else. Just the health officer."