MSP Bob Doris has criticised the council's decision to withdraw more than £200,000 of funding for the Momentum Skills And Pathways programmes and said it was "unacceptable" that "there has been no forward planning."
The schemes have helped hundreds of people return to normal after suffering severe brain trauma or disease over the last decade.
The Evening Times reported last month that the services were to be axed and Mr Doris has put forward a motion in the Scottish Parliament calling for funding to be reinstated.
The motion, supported by 17 other MSPs, stated: "The service provides vital support to people across the city who have acquired a brain injury as a result of strokes, falls, accidents and inherited conditions."
It stated the alternative provided by the council, a programme to help people with mental health problems, "is not particularly appropriate for people with a brain injury, who have very specific and acute needs."
During an emotional meeting yesterday, seven service users and staff met Mr Doris to discuss their experiences and explain the need for the facility to remain.
The MSP now wants to help arrange a meeting between council bosses and NHS executives in an attempt to save the service from complete closure.
Mr Doris said: "What is happening here is the responsibility of the council and the NHS.
"There are people whose postcodes are not within the Glasgow area and their needs are not being met.
"In the long term the Momentum Skills And Pathways programme will save the council, NHS and the Department Of Work And Pensions money because people coming are more likely to need social care if this does not exist."
Frank Beattie, 50, a former construction worker suffered a stroke before being referred to the programme.
He said: "I have come on 90% in the weeks I have come here.
"When I first started I would not talk to anyone, I needed help with my stammer and I had no confidence, but I am completely different now."
The company running Momentum has given emergency funding to allow a reduced service to operate for the next six months, which will allow the current service users to complete their programme and receive some support.
After December the non-profit organisation's funding will dry up and the service will disappear unless funding is secured from elsewhere.
A council spokesman said: "The outcomes achieved by the programme for users were not satisfactory and services can be delivered more effectively elsewhere."