Police said the vehicle had been deliberately driven at the group, and are treating the incident as attempted murder.
The group of five, aged between 12 and 14, were standing on a pavement in Stravanan Road in the Castlemilk area of the city at around 3.30pm on Saturday.
They were struck by a silver Vauxhall Astra being driven by a man. The car failed to stop and drove off towards Birgidale Road.
A 14 year-old girl was taken to Hairmyres Hospital where her condition is serious but stable.
Three girls aged 12, 13 and 14, and a 12 year-old boy were treated for minor injuries.
Detective Inspector Peter Sharp said: “This vehicle was deliberately driven at this group of children and as such we are treating this incident at attempted murder.
“Extensive police inquiries are continuing to trace the man driving the car, his male passenger and also the vehicle involved. Officers are following a number of lines of enquiry.
“At this time I would appeal to any witnesses to this incident, or anyone with information that may assist this investigation, including anyone who may have details of the silver Vauxhall Astra involved to contact police as a matter of urgency.
“There will be additional police patrols in the area to provide reassurance to the local community and I would encourage anyone with information or concerns to approach the officers who will be happy to assist.”
Anyone with information should contact Cathcart Police Office through 101 quoting reference number 2777 of the 24th March. Alternatively CRIMESTOPPERS can be contacted on 0800 555 111, where anonymity can be maintained.