Rockies on Paisley Road West wanted to offer alcohol alongside desserts, which include waffles, pancakes, ice creams and milkshakes.
Peter Lawson, representing the cafe, said the application had been made following requests from customers.
But Glasgow’s Licensing Board has turned down the request, and Cllr Alex Wilson said: “It’s like giving Willy Wonka the licence to sell alcohol in his chocolate factory, it just doesn’t sit well with me at all.”
Cllr Wilson, who represents the Cardonald ward, where the cafe is based, added: “It is great for children and that’s where it falls down for me. I’m not a fan of mixing alcohol, especially when this is an ice cream parlour type of place for kids.
“There is only one other dessert cafe place that does that and that’s in the city centre. For me, to have that in the Cardonald ward doesn’t sit really well with me.
“There’s enough alcohol places within easy walking distance and if families want to go and have alcohol in a place where there are children then there are plenty of restaurants within the area as well.”
Mr Lawson said it was a “very small proposal for alcohol”, with no objections from neighbours or the health board and the alcohol would be kept behind a counter.
“This is for the benefit of parents accompanying children,” he added. “Some people will take their family along to sit there and dad may not want a Knickerbocker glory or whatever.”
The cafe’s opening hours are between 11am and 8pm and Mr Lawson said there was “no question of this turning into some sort of drinking den at a later hour”.
He said: “Customers do look for this, not all of them admittedly, but some of them do.
“My client’s position is that it has been requested, it does happen in other places and the quantity of alcohol will be very restricted. There’s not going to be any spirits, it’s going to be beers and wines.
“It does happen, it’s not a big ask. Will it make any difference to the atmosphere of the place? I doubt not, but I can understand your concerns.”
Mr Lawson then added that people often go for a dessert and a drink after eating when on holiday abroad.
Cllr Wilson said: “I can understand where you’re coming from. I mean the Cardonald ward is very much like Saint-Tropez.
“I’m very proud of my ward. For me, it sits well where it is, it looks fantastic. Children are going in on a regular basis, do we need alcohol alongside ice cream and cake? I’m not convinced.”
Cllr Matt Kerr, who chairs the Licensing Board, and also represents the Cardonald ward, said: “It’s been a great addition to the street, but selling something that is inherently attractive to young people and the idea of combining that with alcohol is worrying.”