The supermarket giant has Ramadan promotions in 239 stores in areas with big Muslim populations.
At Sunshine’s Marketplace Woolworths, posters and a display of nuts and dried fruit greet customers.
The month-long Islamic religious festival involves fasting in daylight hours.
But some customers have complained the promotion is offensive and un-Australian.
Woolworths spokesman Russell Mahoney said the promotion was running in 239 stores around Australia.
“We celebrate as many international festivities as possible to support the diverse population of Australia,” he said.
That included Diwali, Lunar New Year and Passover.
Islamic Council of Victoria secretary Ghaith Krayem welcomed Woolworths’ promotion and said people who opposed such initiatives did so out of ignorance and unsubstantiated fears.
“Ramadan is a time of reflection and renewal and maybe it is also a time for all of us to be inclusive rather than push each other away.”