"We can't say if we have received the complaint yet but we will be investigating it to make sure everyone is aware of our policy," the spokesman said.
The woman said the first words she heard from the staff member were "could you move to the nursing room".
"He wasn't looking at me. He was facing the other direction while talking to me. There was a bit of confusion to begin with as to what he was saying and who he was talking to," the woman told Stuff.
She said she refused to move and the staff member then said, "I would like you to move to the nursing room."
"It wasn't until I got angry and raised my voice that he said, 'I'm just telling you it was over there'," the woman told Stuff.
The mother said he left and no other staff member approached her and she remained in the family area.
She had made a formal complaint to Interislander, she said.
The incident happened while she was travelling on the ferry Kaitiaki to the Marlborough Sounds on December 21.
The Interislander spokesperson said it was not unusual to see mothers nursing wherever they felt comfortable on a ferry.
The spokesperson said he had contacted the company's customer services management and been told it was possible the staff member on Kaitiaki was just pointing out a nursing room was available.
"It's not necessarily well known we have a dedicated room for nursing mothers ... Often they don't like to ask if we have one," the spokesperson said.
The mum posted about the event in a story on her Instagram account.
In the post, which has since expired, the woman said she was "pretty disgusted" by the incident, and described the staff member as "rude" and "very embarrassed (?!) looking".
"After telling him that I can in fact feed my child wherever I please - I was again asked to move," the post said.
"By this point my anger was apparent and your (Interislander) staff member received some colourful language and a little bit of info on the human rights of this country."