It has been reported that the comment was agreed with when Mr Wilson was taking part in a BBC Spotlight programme about the European Union referendum.
The comments were made while BBC reporter Conor Spackman and Mr Wilson were filmed walking around Carrickfergus market talking to members of the public.
At one point Mr Wilson had a conversation with the man out of the reporters earshot, but which was still recorded.
According to the BBC, in part of the conversation Mr Wilson said: “They are doing a programme on the BBC about should we stay in the European Union or get out of it, so I am going around talking to people and then they are going to do an interview with me.”
The man replied: “I’d say get out of it. Between you and me get the ethnics out too.”
Mr Wilson then said: “You are absolutely right, you know.”
When asked about his comments later, Mr Wilson wrote back asking if the BBC was “having a laugh”.
He added: “I am not prepared to spend any more time being interviewed, giving you explanations or responding to what anyone would regard as a disgraceful request to facilitate your biased political slant to this programme.”
A spokesman for the DUP this morning said: “Sammy Wilson is reported to have made comments this morning about ethnic minorities.
“The DUP values everyone who comes to Northern Ireland and makes a contribution to our society. Ethnic minorities are vital to our biggest and best companies never mind our Health Service.
“Get the ethnics out” is a disgraceful phrase. We disassociate the party from the comment made by a member of the public.
“Whilst there needs to be a discussion about how we control our borders, this should be conducted in a factual and respectful manner as part of the EU referendum debates.”