"We don't accept language like 'for both your Pregnancy and Breastfeeding Journey' and the like," he wrote.
"Instead, text must present realistic and accurate information in a neutral or positive way and should not have any direct attribution to people."
Although the advertisement - and another which was blocked later yesterday - remain on the company's own Facebook page, Ms Cooper said they had been blocked from being "boosted" to the news feed inboxes of the page's 21,000 followers.
"I could understand it if there was an offensive image, but it's hardly a nude shot of a pregnant lady."
The second advertisement was for a pregnancy dress, with no mention of breast-feeding.
Ms Cooper, who is pregnant, said she and her mother had spent thousands of dollars on Facebook marketing during more than three years in business and there was nothing new about captions for their dresses.
"This [the first] ad is far from offensive and simply aimed at the target market of over 20,000 people that follow our page."
Her mother acknowledged an image of the dual-purpose dress showed an opening to be used for feeding babies, but said it contained no explicit depiction of that activity.
"How do you alter the wording and still be able to target the market we are selling to?" she asked. "We don't sell anything else."
Action to Improve Maternity campaign founder Jenn Hooper said the Facebook ban was "all a bit silly in this day and age".
"What year are we in, 1800 and what?" she said.
"Women have a right to be informed about all sorts of choices, including when it comes to clothing that makes it easy and accessible to feed their babies.
"Breast-feeding is what it is - it's not penile enlargement."
Ms Hooper said she was aware of Facebook blocking images of breast-feeding, "yet they don't mind when people put all their cleavage and whatever else out there".
A Facebook spokeswoman in Australia said she was investigating the issue with her company's officials in the US.
