The Victoria and Albert Museum has apologised after a mum said she was asked to "cover up" while breastfeeding on a visit to the London attraction.
In a post on Twitter, the woman said she was "perplexed" by the request and posted several images of naked female statues from the museum's exhibitions.
She went on to say she had a lovely day at the V&A "exploring depictions of breasts through the ages".
Its director Tristram Hunt said women may breastfeed "wherever they like".
Tweeting under the name @vaguechera, the woman said: "Flashed a nanosecond of nipple while breastfeeding and was asked to cover up in the V&A courtyard. I am perplexed."
Her tweet has been liked more than 6,700 times and received more than 3,900 retweets, with many people offering messages of support.
The mother pointed out the irony of the request at a museum which displays many statues of naked women.
Posting a photo of a statue showing a man holding up a naked woman, she captioned it: "'I will throw you out of this museum with your naked breasts!' 'But I'm made of marble!' 'Oh sorry you're fine then.'"
The woman told the BBC she was "stunned into silence" by the request from a female member of staff.
She said it was the first negative experience she has had in three-and-a-half years of breastfeeding.
"I had been attempting to be discreet and to feed under a cardigan, but with a distracted one-year-old it can be challenging.
"The staff member was friendly and polite, but obviously asking me to cover up was still intrusive, unpleasant and embarrassing for me, as well as obviously ludicrous."
The mum said she felt it was important to highlight the incident because "the shame and embarrassment caused by that kind of interjection when you are trying to feed could be crushing for a woman who was less Teflon than me".
She added: "It could really badly affect someone's attempt to breastfeed if they were struggling with their confidence."
Mr Hunt, a former Labour MP and shadow minister, apologised on twitter, saying: "Very sorry. Our policy is clear. Women may breastfeed wherever they like, wherever they feel comfortable & should not be disturbed."
The museum also tweeted an apology and said it was investigating the incident, adding: "Women are welcome to breastfeed in the museum & we have quiet spaces for those who prefer privacy."
The museum said its staff received regular customer service training and they will be reminded of their breastfeeding policy.
The woman said she appreciated the apology and that the support she received on Twitter and the museum's response "show that attitudes are on the most part positive".
She added: "That said, clearly not everyone is aware of the legal protection that women are afforded when feeding in a public space.
"Policies are important, but they only work if staff are supported to understand and carry them out."