A Dutch airline is under fire over its breastfeeding policy, after asking one woman to "cover up" as she tried to feed her baby.

Shelby Angel says she was on a KLM flight from San Francisco to Amsterdam in June when a flight attendant gave her a blanket and warned her to cover up if she planned to breastfeed her baby, news.com.au reports.

"Before we even took off, I was approached by a flight attendant carrying a blanket. She told me (and I quote) 'if you want to continue doing the breastfeeding, you need to cover yourself,' " Ms Angel wrote in a Facebook post.

"I told her no, my daughter doesn't like to be covered up. That would upset her almost as much as not breastfeeding her at all.

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Friends of Facebook, please share this far and wide! Here's a warning to all breastfeeding moms: do NOT fly with KLM! A...

Posted by Shelby Angel on Sunday, 14 July 2019

"She then warned me that if anyone complained, it would be my issue to deal with (no one complained)."

Following the incident, a KLM Twitter account later tweeted in response to the criticism they'd received following the woman's Facebook post.

"To ensure that all our passengers of all backgrounds feel comfortable on board, we may request a mother to cover herself while breastfeeding, should other passengers be offended by this," their statement read.

"As an international airline company, we transport passengers with a variety of backgrounds. Not all passengers feel comfortable with breastfeeding in their vicinity and sometimes these passengers complain to the cabin staff."

According to The Guardian, one doctor tweeted they found the policy "offensive".

"I find it uncomfortable and offensive when people chew with their mouths open, infinitely more so than breastfeeding," it read.

"Can you cover up the heads of passengers who do so with a blanket? Thanks!"

In a further statement, the airline said: "We would like to emphasise that breastfeeding is permitted on KLM flights. However, we strive to ensure that all of our passengers of all backgrounds feel comfortable on-board."

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Ms Angels' post was met with thousands of comments, with many saying the policy was "completely unacceptable".

"I have breastfed my son on many flights and never received a complaint from any other passengers or flight attendants," one person wrote.

"I will not use this airline until they change their policy."

"Why can't people that are offended by breastfeeding just choose NOT to look?" another added.