Tyson Whelan, a journalism student at the Royal Melbourne Institute of Technology, said on Twitter a manager in East Doncaster, Victoria, told him "all the registers are out across the state".
A Woolworths spokeswoman said the registers were coming back online now.
Customers were asked to leave many stores after the registers failed to function.
'Everyone was walking out of the store empty handed.
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Numerous customers have shared images on social media of long queues at cash registers and stores that have closed their doors. We were all offered a box of chocolates'.
"We can confirm that an IT issue impacted registers in our supermarkets for a short period of time this afternoon", a spokesperson for the supermarket chain told Computerworld.
Several media outlets have reported that the outage was Australia-wide, and affected all stores, though Woolworths are yet to make a comment.
Chief executive of the company Brad Banducci "apologised unreservedly to customers and store teams for the inconvenience caused".