"Our systems ultimately self-corrected themselves and we were back and open for trade across most stores by 4.30pm, with all stores now operational.
"This type of incident should not occur and we apologise unreservedly to our customers and store teams for the inconvenience caused."
Woolworth confirmed that all stores were now open.
Social media posts showed shoppers banked up in stores with their trolleys, unable to move.
Others were told to leave the stores. Many left full trolleys behind.
The supermarket's social media team responded to the complaints on Twitter by saying IT issues occurred.
The outage also saw some stores pull their shutters down, but it is understood this was a temporary measure taken to prevent more frustrated customers from coming into stores while the outage occurred.
Shopper Sharni was among those asked to leave her groceries behind at the Hampton Park store in Melbourne.
"It was really frustrating. We were all queued up at the checkout and we were told to leave due to a power outage and I just spent an hour doing my groceries," she said.
News Corp Australia counted at least 10 abandoned trolleys and baskets in the store.
A security guard was also stationed at the closed doors to turn shoppers away.
More than 20 shoppers were reportedly turned away by the security guard.
A woman called Rose, from Hoppers Crossing in Melbourne, told 3AW customers were offered lollies as they were asked to leave.
"Everyone was walking out of the store empty-handed. Staff were very apologetic. Staff said every register in every store nation wide has shut down. We were all offered a box of chocolates."
Shoppers took to Facebook across Australia to complain about the outage and accused the supermarket chain of "ruining dinner plans".
One woman, Virginia Johnstone from Sydney posted on Facebook: "Woolworths you are having a laugh ... I just spent 45 minutes shopping with 3 kids and your registers go down and you tell me (quite rudely) that I need to leave the store without my groceries.
Thanks for dinner Woolworths - Bankstown
Posted by Bint Abi on Sunday, 15 April 2018
"Good customer service would have been to let everyone currently in the store have their trolley load for free. But no ... you throw everyone out on school holidays with nothing for dinner. Bad form ... I'll stick to Aldi."
Woolworths has 995 stores across Australia, which means the outage affected close to 500 stores.
- News.com.au