Holly Mayes, 21, was in the pool at Billing Aquadrome in Northamptonshire when her four-month-old son Vincent began crying because he was hungry.
The new mum took herself into the corner of the swimming pool to breastfeed, but was soon told by a female lifeguard to remove herself from the pool, because others were feeling "uncomfortable" and it was "unhygienic".
A spokesperson for Billing Aquadrome said in a statement: "As a family holiday park we keenly welcome new mothers and we fully support women breastfeeding in public places, in line with current legislation.
"We will investigate the incident and we apologise for any inconvenience caused."
The spokesperson continued: "Mums have every right to feed their babies when they need to do so and our operating practices are to encourage breastfeeding in a safe and comfortable environment for both the mother and child.
"In this case, as there were a number of other users in the pool, swimming, playing and splashing, the lady involved was invited by a female lifeguard to move to the side of the pool, or to the changing rooms.
"At no stage was she asked to refrain from breastfeeding her baby in public."
Legally, women have the right to breastfeed in public places unless there are health and safety reasons to stop.
Speaking to ITV News when describing the incident, Mayes said: "I felt like I was being made [to feel] I was doing something wrong and I felt ashamed."
Mayes was told by the lifeguard that breastfeeding in the pool was "unhygienic", however she said her son was high enough above the water that he wouldn't drink any chlorine.
She told The Northampton Chronicle: "I was so shocked. I explained that I had every right to feed in a public place and she [the lifeguard] said that, if that was the case, then she was very sorry and I should talk to a manager.
"I did that and he apologised profusely and offered my free entry to the pool for a year."
Since the incident happened, a breastfeeding group in Northamptonshire has defended Mayes.
Esther Stimpson, Co-chair, Northamptonshire Breastfeeding Alliance, told ITV: "With regards to the hygiene aspect, breast milk really is the last thing we should be worrying about in a swimming pool.
"Pregnant and breastfeeding mothers will be lactating anyway and could leak milk into the pool at any time.
"Babies can be sick at any time, not just if they're breast-fed, so for us it's not a concern. The baby was being comforted and reassured and being fed at the same time."