Officers were called to a store in Chullora, in the south west of Sydney, on Saturday morning following reports of an altercation.
Video of the incident was shared widely online.
Australia has been affected by panic buying of supplies - particularly toilet paper - due to fears over the spread of coronavirus.
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New South Wales state police acting inspector Andrew New said: "We just ask that people don't panic like this when they go out shopping.
"There is no need for it. It's not the Thunderdome, it's not Mad Max, we don't need to do that."
Two women, aged 23 and 60, from the Bankstown area of the city have been issued court attendance notices for affray and are due before Sydney's Bankstown Local Court on April 28.