Many people began experiencing difficulties in the late afternoon on Tuesday, despite more than 1.3 million having successfully completed the Australian Bureau of Statistics' online form, until the site crashed completely around 7.30pm.
The ABS has confirmed the temporary outage was due to the high volume of users accessing the site.
Those experiencing error messages and other issues with the website took to social media to complain.
One Facebook user said "is it just me or is the census offline?" while others vented their frustration using the hashtag #Censusfail on Facebook and Twitter.
"The #census2016 site is down. A quick census of the people in my house revealed no one was surprised to hear this," Facebook user Tom Taylor said.
The ABS responded by advising callers to wait until Wednesday to contact the hotline "when (they) expect calls to reduce", assuring people they will not be fined if they do not complete their census on Tuesday night.
The 2016 census has been fraught with contention after it was discovered the ABS would be holding onto data for four years instead of the standard 18 months.
However, the ABS has promised private information will not be released.
The promise has come after several senators, including independents Nick Xenophon and Jacqui Lambie and Greens Scott Ludlam and Sarah Hanson-Young, vowed to risk the $180-a-day fine by withholding their names and addresses amid privacy concerns.
An error message some Australians received. Source: Supplied
Former NSW deputy privacy commissioner Anna Johnston is refusing to fill in the census at all, despite census head Duncan Young repeatedly promising that everyone's data will remain top-secret.
"Hand on heart, the security set-up in order for people to submit their information - it's encrypted all the way through from their browsers into the ABS's internal environment," he said.
"Then we go through the process of separation. The information is isolated so people who can access names can't access the rest."
While Australians have until mid-September to complete the census without incurring a fine, the ABS said people were still encouraged to fill out the form as soon as they could.
About 1.3 million people successfully completed the form until the outage at around 7.30pm (AEST) on Tuesday.
The ABS confirmed the crash was due to the high volume of users accessing the site.
