Farage, leader of Euro-skeptic party UKIP, told LBC radio that public breast-feeding makes some people uncomfortable, and women should do it "in a way that is not openly ostentatious."
He spoke after a mother, Louise Burns, said staff at upmarket hotel Claridge's asked her to cover herself and her baby with a napkin while feeding her in a communal area.
Farage said the hotel had the right to make its own rules, including asking such women to "perhaps sit in the corner."
The comments drew a barrage of criticism.
The prime minister's office said David Cameron did not agree. Downing Street said "breast-feeding is completely natural and it's totally unacceptable for any women to be made to feel uncomfortable when breast-feeding in public."
Justine Roberts, chief executive of parenting website Mumsnet, said breast-feeding is "a natural, essential human process and those with an issue simply need to get over themselves."
"Babies need to be fed when they're hungry, and there's nothing ostentatious about a mother responding to that need," Roberts said.
Farage later released a statement saying, "I personally have no problem with mothers breast-feeding wherever they want."
But he said that if hotels want "to maintain rules about this stuff, then that is up to them, as it should be."Suggest a correction