Helen Moran, 44, was left with horrific injuries after falling 30ft and suffering two blood clots on the brain.
She campaigns for better awareness of brain injuries - and believes Glasgow City Council should be pushing cyclists to wear helmets when they hire bikes.
The city's £600,000 scheme was launched in June and means 400 bikes are available for public hire at 31 locations across the city.
Ms Moran said: "Living with a traumatic brain injury is incredibly hard and people do not realise how easily it can happen or what a devastating effect it can have on your life.
"The Nextbike scheme is sending hundreds of people out riding bikes through Scotland's busiest city without helmets on, which is reckless and careless.
"The council will say lending bike helmets is too difficult but I am sure there is a way around it to ensure the safety of cyclists.
"It is ridiculous bike helmets are not available with these bikes. It makes me furious to see it."
Her call is backed by charity Headway Glasgow, which is part of the UK-wide brain injury organisation Headway.
Simon Glen, of the charity, said: "Headway wants to encourage healthy exercise in a safe way and we support the Highway Code, which says cyclists should wear a helmet.
"We understand the problem of shared helmets and possible hygiene issues involved, and also that helmets might be more easily stolen than the bikes.
"However, we believe the message that helmets should be worn should be prominently displayed on the Nextbike stations around the city, and given more prominence on the Nextbike website.
"The advice is on the website but you need to search to find it - that is not good enough."
Ms Moran, who has two children, Ryan and Cian, fell from the balcony of her first floor flat in Charing Cross while sleepwalking in 2006.
She developed two blood clots on the brain, and also suffered a broken pelvis and ribs, a burst spleen and liver damage.
Doctors told her family she was unlikely to survive after brain surgery to remove the two clots.
Although she has amazed medical staff with her progress she said life with a traumatic brain injury is a struggle.
And she does not want to see anyone else suffer a similar fate - particularly children.
Ms Moran added: "One of the things that really bothers me is the bad example this sets to young children."
A Glasgow City Council spokesman said: "Current legislation states there is no requirement for cyclists to wear helmets.
"In addition, there are a number of practical reasons why the council can't supply helmets: they need to be replaced after being dropped and if we are unaware of any helmets being damaged we may unknowingly provide helmets that are not fit to be used.
"There is also the problem of different sizes for cyclists because loose- fitting helmets go against Highway Code guidelines."