The Commission for Racial Equality in Wales says it will write to Thomas Cook asking the firm to explain why staff have been asked not to speak Welsh.
The firm said it must ensure "clear communication at all times"
Staff at the travel agents' Bangor shop in Gwynedd have been told all work conversations must be in English.
The firm told staff they must conduct business conversations in English, as it is the UK's common language.
The Welsh Language Board said it was "disappointed" and it would ask the company to change its position.
It emerged last week that staff at the Bangor store - one of the areas of Wales where Welsh speaking is strongest - had been asked to use only English in business.
A Thomas Cook spokeswoman confirmed the policy applied to all non-English languages.
Concerns were raised in the Bangor travel agent
A company statement said: "Thomas Cook requests that all staff speak English 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.
"Thomas Cook employs staff from many cultural backgrounds, therefore the company appreciates its staff may want to talk to colleagues in other languages for anything that is not business related".
The Commission for Racial Equality in Wales has warned that the policy might be in breach of the Race Relations Act.
Wales Commissioner, the Reverend Aled Edwards, said the promotion of good relations was their "paramount concern".
He would not comment on the particular case, but added: "The Commission for Racial Equality does have a power to investigate through its legal committee and also if it sees fit to start a formal investigation but I think common sense and courtesy would be the best option."
Meri Huws, chair of the Welsh Language Board, said there was "disappointment" that a large private sector company had decided to take this decision.
She said the Welsh Language Act does not cover the rights of the individual in the work place.
But she added it was "a very surprising decision, in the light of the number of private sector companies, large and small, that are choosing to use the language in terms of marketing, in terms of services to their customers, and generally in day-to-day work place activity".