The incidents happened over the course of just two weeks and have significantly cut the number of Just Eat Cycles available to rent.
They are believed to have been concentrated in the north of the city and Leith.
The normal 500 available bikes has been reduced to around 200.
It follows at least 25 bikes being seriously damaged and ten stolen in February.
Cycles were also withdrawn from Victoria Park in Newhaven in December after being twice hit by vandals and thieves. Bike stands were also vandalised in Easter Road, Leith, in January.
Just Eat Cycles told The Scotsman: “There has been a drop off in bikes on the streets, predominantly down to increased instances of vandalism.”
It described most of the damage as “minor and repairable”.
However, a spokesman said more severe damage had been caused to some bikes at “dockless” hire stations where they are not physically attached.
He said: “A smaller portion of bikes have had their front wheel locking mechanism damaged by individuals attempting to forcibly unlock bikes at virtual stations.
“Just Eat Cycles is working with the police to reduce instances of this happening.”
It is believed repeat attacks by youngsters are to blame.
One source said: “Anecdotally, the people doing the damage are teens/kids running wild and targeting the same spots – typically around Leith and north Edinburgh.”
Just Eat Cycles said the latest spate happened after it offered free hires for a week earlier this month.
General manager Charles Graham said: “We experienced a rise in user activity in the weeks before the free week and a significant spike in activity during the free week itself.
“This has unfortunately led to a number of our bikes being intentionally damaged and in need of repair.
“We are now working to repair and return these bikes to hire points across the city as quickly as possible in order to return the fleet to over 500 bikes.”
Ian Maxwell of Spokes, the Lothian cycle campaign, said: “There may be other things the operators can do to reduce the risk of this happening, such as altering where bikes are located.
“There may also be ideas from established UK hire schemes on how to cut vandalism.
“This may be particularly necessary when the more expensive electric bikes become available.”
Edinburgh City Council transport vice convener Karen Doran said: “Vandalism of any form is unacceptable, and to purposely damage bikes meant for the use and enjoyment of the public is particularly disappointing.”
Cycling Scotland, the Scottish Government-funded development agency, said: “A bike hire scheme is a public service, just like public transport, and can be a great way for people to easily access bikes and the benefits of cycling.
“We hope the bikes can be quickly fixed, back in use and accessible for everyone.”
Glasgow City Council said there had been few attacks on its scheme since initial incidents when it was launched.
A spokesman said: “There were some instances of vandalism when the scheme was introduced in 2014 but since then vandalism to the bikes has been negligible.”