Heather Vaughan, 29, was feeding her nine-week-old baby Lydia during a visit to the National Museum of the Royal Navy in Portsmouth when she was approached by a member of staff.
"He quite angrily pointed to me and said, 'We don't do that here, there are baby toilets you can go and do that in,'" mum-of-two Heather told Heart radio.
"He came up to me in front of another family and spoke to me so rudely, I was just ashamed.
"I was just so mortified and embarrassed, I felt victimised. My emotions just got the better of me, I just broke down. It took me all day to calm down from that incident."
It was Heather's first full-day outing with her daughter and the confrontation upset her so much that, in order to avoid having to feed in public again, she cut their trip short and headed home with her husband Daniel and son Josh.
The Director General of the museum has since apologised for the incident.
"We are very sorry to Mrs Vaughan for this mistake and error in judgment from one of our team," said Dominic Tweddle.
"Our member of staff became confused and is deeply and sincerely sorry for his comments and reactions. This incident is not representative of him or our organisations and we all regret the distress caused."
Dominic stated that the museum is committed to improving staff training to ensure an incident such as this will not occur again.
More on Parentdish