In pictures supplied to the Yorkshire Evening Post, trolleys were abandoned and queues were the length of the aisle in the Kirkstall Morrisons store.
Leeds residents also took to social media to complain of large queues in other supermarkets including Asda and Tesco.
Supplies of toilet roll, hand gel and pasta are all running low at the majority of retail outlets.
One woman, who wished to remain anonymous, told the Yorkshire Evening Post that she queued for more than half an hour to get groceries.
She said: "It was complete madness.
"I had about 20 people in front of me, every queue was the same.
"There was barely anything on the shelves.
"Everybody was complaining and some just dumped their trolleys.
"I have never seen anything like it."