Liz McPhail was left stunned when staff refused to give her hot water to heat up little Madison's food at the Leisuredrome in Bishopbriggs, near Glasgow.
The 42-year-old, a mother-of-four, said another customer who had been feeding her toddler with her own food, was also told to move.
There are no health and safety regulations which prevent catering establishments from helping parents prepare food for their children.
The Leisuredrome is run by East Dunbartonshire Culture and Leisure.
Liz, from Lambhill in the north of the city, said: "They said the refusal was down to health and safety reasons - in case the water was made too warm.
"It think it's discrimination against small children. Don't tell me I can't feed my daughter.
"There was a woman next to me, she brought her own food and she was told to leave.
"If you are not allowed to heat the food in a family-orientated place they should provide baby food. There are a lot of places that are not providing an alternative."
Some supermarket cafes provide parents with a microwave where they can heat food "at their own risk".
Liz, whose other children are aged 18, 20 and 25, said: "I can't believe how much things have changed.
"I come from a big family and I'm used to taking babies into cafes. We are just not very family-orientated in this country."
Liz said she had also experienced problems feeding her baby in cafes in the city centre.
Last year a Government panel set up to counteract over-the-top health and safety rules found that some cafés refuse to warm up baby food or supply hot water, because they say it's just too risky.
The panel asked the public to send in examples of bizarre health and safety restrictions so they could assess if there was a genuine risk.
Judith Hackitt, chairman of the Health and Safety Executive, added that some of the examples were "blatant and disturbing examples of people using health and safety as an excuse."
Mark Grant, general manager of East Dunbartonshire Leisure and Culture Trust, said: "It was unfortunate that our catering contractors weren't able to provide the hot water and we apologise for the inconvenience, but they felt it was unsafe to provide hot water that had not been heated to the correct temperature.
"We are committed to being a baby friendly leisure centre and on the back of this incident, it has been agreed with our contractor that baby food warming facilities will be installed to ensure customers visiting the centre can do so in the peace of mind that they can heat babies' food.
"These facilities will be put in place as soon as possible."