Other staples such as bread, meat, rice and pasta were also snapped up.
Photos and videos have emerged online showing trolleys stacked with rolls of toilet paper and stores packed with people.
Coles introduced temporary restrictions on toilet paper for the City of Sydney, Randwick, Waverley and Woollahra local government areas on Friday.
The move came after the first set of lockdown restrictions for those areas were announced, with limits of two packs of toilet paper per customer.
The supermarket chain is yet to announce if those limits will be extended to include the new lockdown areas.
Woolworths is yet to announce any new product limits for NSW.
When announcing the lockdown, Berejiklian assured residents there was "no need to panic buy", noting that supermarkets would be open throughout the whole lockdown period.
"You're allowed outside to purchase goods, essential goods and services and I appreciate people following these instructions," she during yesterday's press conference.
"There is no need to panic buy. All the shops will be open every day of the week.
"There is no curfew. You can leave your home at any stage to purchase any essential goods that you need to and that is a given."
She urged people to be "thoughtful and considerate" about their fellow citizens, emphasising that there was no reason at all to rush out and stock up.
There were also reports of panic buying on Thursday before any lockdown restrictions had even been announced.
As Sydney's Covid-19 cluster rose, there were multiple shoppers reporting their local Coles or Woolies had either been stripped bare or were running low on toilet paper.
Condemnation of the panic buying has was swift, with several tweets pleading with people not to stockpile.
"I am still wondering why do people think toilet paper needs to be completely collected off the shelf every time there is a lockdown?" one person said.
"This happened even when the shops guarantee that there are millions of rolls more in the pipeline and no one will ever run out. Madness."
"Not panic buying toilet paper again Sydney," another person wrote.
