People who shop at Sainsbury's in Hereford have been described as "pikeys" by a senior manager at the supermarket.
Sainsburys are trialling new beauty departments
Lisa Collins, who is in charge of the company's health and beauty section, made the comments while addressing a recent conference.
She told her audience Sainsbury's had tried new in-store health and beauty departments in two "comfortable" areas of the country - Solihull, West Midlands, and Leamington Spa, Warwickshire.
Ms Collins said the company was to use the idea in other UK stores, including the one in Hereford, adding: "Or, as we call them, our pikey customers."
She is obviously a very stupid woman who has been promoted above her station
Ms Collins also mentioned supermarkets at Cobham in Surrey, and Croydon in south London.
According to the Oxford Dictionary of Slang, pikey dates back to 1847 and means gypsy or traveller.
The word is believed to be a contraction of "turnpike" - a reference to a feature of the travelling life in years gone by.
Councillor Terry James, leader of Herefordshire Council, said Ms Collins' outburst was ignorant and offensive.
"I find her comments extremely insulting.
Sainsbury's takes this very seriously and cannot condone it
"She is obviously a very stupid woman who has been promoted above her station."
On Tuesday Ms Collins, who has apologised for her comments, refused to answer any questions about the matter.
But a Sainsbury's spokeswoman claimed the executive was not aware of what pikey meant when she made the comment.
"I know that she did make these comments at the conference," the spokeswoman said.
"I think it was an off-the-cuff, very flippant thing and she is deeply distressed and regretful.
"We are looking into the matter but Sainsbury's takes this very seriously and cannot condone it. We are talking to her at the moment."
Ms Collins made her remarks at a conference organised by the Institute of Grocery Distributors on 13 March.