The move sparked anger among cycle campaigners, who said it was ridiculous that cyclists would have to travel slower than parks’ vans.
There is currently no speed limit for cyclists in the council’s 90 parks, which are seen by many as safer and more direct routes across the city than roads.
The council’s draft new parks management rules stated: “Cyclists must maintain proper control of the cycle and ensure they do not endanger other road users. Cycle speed should not exceed 5mph.”
The rules also state: “Where permitted, vehicles must be driven safely and must not obstruct or risk causing injury or damage to other road users. Vehicle speed must not exceed 10mph.”
Dave Brennan, an organiser of the annual Pedal on Parliament event to highlight cycle safety to MSPs, said he had been initially “speechless” at the plan.
He said: “What I think this does is illustrate the regard that Glasgow City Council has for the pedal bike.
“It is seen as a nuisance, an inconvenience, something that has to be discouraged and, if you absolutely have to plan for it, make sure it is added on at the very end of the planning process, as it can just fit around all the other far more important modes of transport.”
A council spokesman said: “We want to ensure people can enjoy the parks without being caused any nuisance, and park users behave in a safe and responsible manner.
“At the moment, we’re suggesting cyclists stick to a 5mph speed limit in parks to ensure other parks users’ safety.
“We would encourage cyclists and cycle groups to get involved in the consultation and give us their feedback.”