Officials say the ban at Queen's Park is designed to deter rats at the popular South Side park.
Signs posted around the pond urge visitors not to feed the ducks because it "attracts vermin". The posters also threaten a £50 fine.
Council bosses have defended the controversial decision.
A Glasgow City Council spokesman said: "It is important that visitors to the park can enjoy it safely. Although there are currently no signs of vermin in the park, feeding the ducks has been shown to attract vermin in the past. We would urge people to ensure the park remains a safe and enjoyable place for all and not feed the ducks."
Generations of families have visited the pond at the heart of the park to feed the birds.
And some are unhappy about the ban on the popular pastime. One female park user, who did not wish to be named, said: "People have been coming here for years to feed the ducks, so why bring in this rule now?
"It's completely over the top. There must be a better way to tackle any problem than banning children from feeding the ducks."
The vermin, which are attracted by bird food and rubbish, can spread a wide variety of diseases, including potentially fatal Weil's disease and food poisoning.
Officials have also been investigating claims that people have been seen dumping bags of unwanted food in the park.
The issue previously came to light when the park was hit by a plague of "giant" rats. Infestation control teams were called out in 2011 to tackle the outbreak.