Travel agent Thomas Cook's request for Welsh speakers to discuss work in English "probably" breaks the law, says the Commission for Racial Equality.
Its staff in Bangor, Gwynedd, were told that all work-related discussions with colleagues must be in English.
Protesters demonstrated outside the store with tape across their mouths.
Thomas Cook said its staff had not been banned from speaking Welsh, or any other language, privately.
Cymdeithas yr Iaith (the Welsh Language Society) said it highlighted the need for a new Welsh Language Act.
It has emerged that staff at the Gwynedd store had been asked to use English only to discuss business matters, such as training and team performance.
In a statement, Thomas Cook said the policy did not apply to personal conversations between staff, nor did it apply to Welsh-speaking customers wishing to be served in Welsh.
The statement read: "Thomas Cook can confirm that its staff have not been banned from speaking Welsh - or any other language - in its network of UK stores.
"The company has always requested that its staff, regardless of any geographical location, speak English to other staff members when discussing work-related matters in the work place.
"This ensures clear communication at all times and is respectful to team members who do not speak other languages."
A bilingual sign has now been put in the window of the company's office in Bangor which reads: "Despite press reports you are very welcome to do your business here through the medium of Welsh."
The Commission for Racial Equality in Wales said it would be consulting its lawyers, while the language society has already been in contact with the firm.
Commission director Chris Myant told BBC Radio Wales that Thomas Cook's policy was "quite probably" in breach of the Race Relations Act.
He said: "It's somewhat silly. It's not something that will work in the workplace.
"We won't make a definite statement until we've actually seen the full details. But this is something that won't run with the Race Relations Act in general."
Hywel Griffiths, chair of Cymdeithas yr Iaith Gymraeg - which translates into the Welsh language society - said the decision was "disgraceful".
"It really wouldn't have happened if a [new] Welsh Language Act had been in force," he said.
"If you've got customers coming in speaking Welsh, employees who are fluent, then they have a right to speak whatever language they wish in the workplace."
Education Minister Carwyn Jones, who is responsible for Welsh language policy, said the bar was "totally unacceptable" and asked to meet the company.
First Minister Rhodri Morgan said while there needed to be "changes" to the Welsh Language Act, he did not believe a new law was necessary.
"We don't necessarily need a new Welsh Language Act, but what we need to do is strengthen the rights of individuals to avail themselves of the language act as it exists today," he said.
"Or, we need to strengthen the ability of individuals to take on a company that is treating them in a way that cuts across a bilingual Wales."
Meanwhile, Plaid Cymru's parliamentary leader, Meirionnydd Nant Conwy MP Elfyn Llwyd, said the ruling showed "crass insensitivity" and deserved to be "hammered economically" if it did not change its policy.