Once signed in to the new app, users are able to scan QR codes at businesses, public buildings and other organisations to track where they have been for contract tracing purposes.
But Google has been inundated with frustrated users unable to even log in.
"Trouble logging in got error as others got, when loading details. Had to reset password. Still issues," one user said.
Another wrote, "I can't even get through the sign up stage. Password needs to be ridiculously long, and once you have that sorted you're sent a verification code, exiting the page to access verification code from your email."
One person said they couldn't create an account due to it not accepting "email verification code".
"Please stop wasting taxpayers money and get it fixed. And I should be able to use my Google/Facebook/MS account to login instead of create a new user account."
The ministry spokesman said all feedback was welcomed.
"It is entirely normal for any new app to have some bugs or issues when it is first released
"The ministry encourages anyone using the app who encounters any issues to send their feedback to tracingapp-feedback@health.govt.nz."
It was reviewing all feedback as it came in so it could help fix bug fixes and patches to the app.
"The first fixes will be deployed early this afternoon, and we will continue to monitor feedback and address issues as they arise," the spokesman said.
Director general of health Ashley Bloomfield said the app would help identify, trace and isolate cases and close contacts to prevent further spread of Covid-19.
As for what happens to people's privacy and data, the app lets the user control their information.
"Any information you decide to record with the app will be stored securely on your phone and deleted automatically after 31 days.
"It's your choice whether you share any of this information with contact tracers, and any information you do share will be used only for public health purposes and never for enforcement.
"Like all mobile apps, NZ Covid Tracer will be updated over time as new features are developed. In the next release, NZ Covid Tracer will be able notify you if you have been at the same location at the same time as someone who has Covid-19 and will allow you to send your digital diary directly to the National Close Contact Service."
Privacy commissioner John Edwards welcomed the new app which was "a privacy-friendly solution for contact tracing which New Zealanders should feel secure in downloading and using".
The ministry consulted his office during the development of the app and conducted a privacy impact assessment, he said.
"I want to assure New Zealanders that this app was created using Privacy by Design principles which put privacy at the foundation of the process.
"Contact tracing apps are an emerging technology for tracking and managing pandemics. For them to work well, a high percentage of the population needs to use them. The more people who use them, the more effective they will be."
He said the information collected by the app is held for public health purposes only and not shared with any agencies other than for contact tracing purposes.
Professor Dave Parry, head of Department of Computer Science, Auckland University of Technology, said the app was "relatively simple" to use.
He said the Singaporean and Australian apps used Bluetooth to detect who you have been in contact with – as long as they also had the app.
"Bluetooth apps can only give approximate distances to other people and usually need more power, meaning you have to charge the phone more often. They also need everyone to use the app and usage has been very low at around 10-15 per cent in Singapore."
With the Government's app, it was "technically much simpler" as it uses a QR code to "check in" to places.
"We are already doing this recording as we check-in to shops, etc. However, because there are many different apps and paper-based ways of doing this, getting the data quickly to the contact tracing team is hard, and following up contacts quickly is very important so that they don't infect others."
However, the "biggest issue" with the app was that it didn't bring much benefit to the user and the set up was found to be "rather clunky".
"It doesn't replace the check-in systems to businesses or even allow you to automatically send your history to the contact tracing team, although this is promised. I found the interface to set it up rather clunky and I suspect a lot of people will give up."
Its advantages were that it supplied exactly the information needed for contact tracing, should use less power than Bluetooth, doesn't release private information.
"It depends on people checking in accurately, although I think most people will be happy doing that although the onus is on you to remember to do it."
Bloomfield said people would also be able to self-report any Covid-19 symptoms so they could be tested for the virus if appropriate and complete a daily health check-in through the app if in isolation.
"I encourage all New Zealanders to download the NZ COVID Tracer app to help protect yourself, your friends, whānau and community by making it easier to trace the people you've come into close contact with."
* NZ Covid Tracer is available now from the Google Play Store and the Apple App Store. Further information about the app can be found at www.health.govt.nz/NZ-COVID-Tracer.