In an open letter posted on Facebook, Jessica Coakley Martinez, who was travelling without her eight-month-old son, said she felt "humiliated".
"You made me dump out nearly two weeks worth of food for my son," she said.
Heathrow says the UK government's rules on carrying liquids on planes are set out for passengers on its website.
The rules, set out by the Department for Transport, say that liquids may only be carried in containers holding 100ml or less in a transparent and re-sealable single bag.
Martinez wrote that, although she should have looked up the rules, the regulation that breast milk was not allowed if the mother was travelling without her baby was "incredibly unfair and exclusionary in consideration of all of the other working mothers like me".
She wrote: "If I acted irate, it's because it was the only appropriate reaction I could muster.
"I now don't have the option to solely breastfeed my son because I don't have enough milk to supply him while I'm at work, despite all of my best efforts.
"Security is the priority, but it isn't and shouldn't be your only goal, and it certainly shouldn't punish those you intend to protect.
"Beyond literally taking food from my child's mouth, you humiliated me and made me feel completely defeated as a professional and a mother."
Rules restricting the amount of liquids which can be carried as hand luggage on flights leaving UK airports were brought in after the discovery of a terrorist plot to detonate liquid explosives on board seven transatlantic airliners in 2006.
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