The group of four were photographed in a Coles store in the small town of Woodend outside of Melbourne.
CCTV images of the group inside the supermarket, believed to be from October 26, was obtained by The Age.
The group – two men and two women believed to be in their early 20s – were wearing swastika armbands and other features of the Third Reich’s uniform, including the imperial eagle.
When told by another shopper that their uniforms could be offensive to Jewish people or Holocaust survivors, they reportedly told a concerned person to “f*** off” multiple times.
Craig MacKenzie, a concerned resident, saw the group and told The Age he confronted them about what they were wearing.
Mr MacKenzie explained they seemed to be heading to a party and didn’t expressly identify themselves as white supremacists or Nazis.
He said other shoppers, including numerous elderly people, were intimidated by the display.
“Once in the supermarket, I said to them that they were being highly disrespectful and had no idea what their uniforms meant,” Mr MacKenzie said.
“The blokes told me that it was ‘only a joke’ and to f*** off. I persisted, saying that there could be people here who went through World War II and the Holocaust. They laughed it off and told me to f*** off again.”
Jennifer Huppert, the president of the Jewish Community Council of Victoria, said there is a “lack of “understanding” about Nazi memorabilia and the widespread offence it can cause.
Jewish groups have warned that anti-Semitic attacks in Australia are on the rise.
The incident has caused outrage online, with some calling for the group to be “named and shamed”.
It has been described as “beyond revolting” by Dr Dvir Abramovich, Chairman of the Anti-Defamation Commission.
“For many (it) would be as frightening as being confronted by a gun,” Dr Abramovich told Yahoo News.
“The wearing of the Nazi uniform is an incitement to violence and murder, it is a call for a world without Jews, plain and simple.”