The retailer said its policy is for staff to speak in English to customers, irrespective of their native language.
It comes after two staff members in Scotland were banned from speaking Polish to each other on their tea break.
The store said it was to ensure all its staff and customers "felt comfortable".
"It is Lidl UK company policy that staff speak in English to customers, irrespective of their native language," the company told the BBC Welsh-language website Cymru Fyw.
"This is for the benefit of all our customers as well as our staff to ensure a comfortable environment where all feel included.
"However, it goes without saying that our staff are able to assist a customer by conversing in their native tongue, if the customer is unable to speak any English."
The Welsh Language Society (Cymdeithas yr Iaith) said the policy was "appalling".
Its chairman, Jamie Bevan, added that "since the Welsh language bill was passed four years ago, it is illegal to stop staff from speaking to customers in Welsh".
Welsh Language Commissioner Meri Huws said she will respond in due course.
The Welsh government said: "The Welsh language has official status in Wales, and there are provisions in the Welsh language measure to protect people's freedom to use the language.
"The Welsh language commissioner has the power to investigate any allegations of this and can produce reports for Welsh ministers to consider."
Staff at Lidl supermarkets are being stopped from speaking any language other than English in their UK stores - including Welsh.