A photo of the promotion, which advertised a 38 per cent discount for certain beef products, was uploaded by a Twitter user @AdamFlinter on Monday.
"Cold Storage's #deepavali promotion was on beef!!! Cultural understanding eh?" he wrote, adding that the photo was from a friend.
Deepavali or Diwali was celebrated in Singapore on Saturday, October 29, with a public holiday.
Hindus in Singapore celebrate Diwali in a grand style with banners and buntings displayed across Little India - a precinct of Indian businesses, eateries, motels and hotels.
It added: "We have since explained and coached him on the cultural sensitivity and he assured us that he had no intention to disrespect the Hindus. We also took this opportunity immediately to coach all our team members to be mindful of cultural sensitivities in Singapore."
"We sincerely apologise to all Hindus who are celebrating Deepavali on this matter," said Cold Storage, which has more than 100 years of history in Singapore with stores in Malaysia and Indonesia.
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