The new rules would slow cyclists to walking pace and have been described as 'ridiculous and unenforceable.'
As part of their Park Management Rules consultation, Glasgow City Council's Land and Environmental Services want to encourage park users to enjoy parks and open spaces "safely and responsibly."
Under the proposal, cyclists have been warned not to endanger other road users and will only be allowed to cycle on tarmac paths or roads, designated cycle tracks or mountain bike courses.
Already, the council is facing a backlash from cyclists, who say the speed cap will discourage people from getting on their bike.
David Brennan, cycling campaigner for Pedal on Parliament, has warned the speed limit could be unsafe.
He said: "Anyone who cycles knows it is difficult and actually quite unsafe to keep your balance on a bike at that speed. Even my four-year-old goes faster than that.
"This seems to demonstrate a wider attitude held by the council that cycling is just a nuisance.
"If you look at the new Fastlink transport routes, cyclists are a mere 'shoe-in' in the development, when only 50% of Glasgow households own a car."
While bike speeds would be capped at 5mph, motor vehicles in parks would have a maximum speed of 10mph.
Jim Ewing, project manager for cycling charity FreeWheel North, agreed that the speed limit is unworkable.
He said: "This rule would definitely stop people from cycling in parks.
"I'm not aware of that many cycling accidents happening in green spaces which would bring this on.
"Why should cyclists be penalised any more than runners are? I think 10mph is a more reasonable limit for everyone."
In November, the Evening Times told how Glasgow was ranked as one of the top performing councils in Scotland when it came to cycling.
The study, by Cycling Scotland, analysed the performance of every Scots council in developing policy to get more people on their bikes.
In October we revealed that the number of cyclists in the city centre has increased by 133% in the last five years to 7000 annually.
But cyclists on a popular commuter route in Kelvingrove Park said the speed limit could put people off taking to two wheels.
Carolyn Butler, 22, a dental student from Aberdeen, said: "I agree that cyclists should be more aware of their speed and people's safety, but there are probably better ways they could improve it — like road signs or better cycle paths."
Gregor McMillan, 41, an architect from Kilsyth, agreed that there would be better alternatives to the speed limit.
"It wouldn't be so bad if we had better cycle paths. The ones we have on the roads on the moment have a lot of potholes."
The move comes just months before work is due to start on a new, £10 million cycle route in Edinburgh, as a legacy to the Commonwealth Games.
A lot of work has been done in the city to promote cycling in the run up to Glasgow 2014, including the Connect 2 scheme, which helped to complete the Bridge to Nowhere over the M8 and connect cycle routes from Kelvingrove Park to Glasgow Central Station.
Ian Aitken, chief executive of Cycling Scotland, said: "Parks and open spaces are also places where many different people visit to enjoy the outdoors, and therefore everyone needs to use these spaces responsibly and considerately.
"Rather than a prescriptive approach, Cycling Scotland recommends more of a focus on common sense, such as that found within the Scottish Outdoor Access Code and Scottish Canals' Towpath Code of Conduct, to make sure that all users of Glasgow's parks and open spaces adapt their behaviour to take consideration of others."
A spokesman for Glasgow City Council insisted it was consulting the public before setting the new rules.
He said: "We want to get feedback from cyclists and other park users on the proposal.
"But above all, the rules aim to make the park safer for everyone."