The I Can Therapy Centre on Ecclesall Road opened in late February 2019, but bosses say that it is no longer economically sustainable.
The centre is used by people with a range of injuries and disabilities, who say it helps them with both their physical and mental health, and allows them to socialise with others.
The news was greeted with dismay by member Marie Hallam, who says the centre’s closure will leave a big hole in many vulnerable people’s lives.
She said: “I got polio when I was one and I use it to exercise but there are people who have had strokes who use it and others in wheelchairs.
“It is really valued and people are very upset about it. They should have contacted us to tell us what the situation was and what our options were.”
A public meeting this week saw members discuss proposals for saving the centre including accessing charity or NHS funding.
Marie added: “We haven’t even been approached to see if we can pay a bit more. We are asking them to let us use it until January 31 just to give us a bit of room for manoeuvre.”
Kevin Patterson, chief executive of Valley Leisure, said: “Valley Leisure is an independent, self-funding charity and we have applied our charitable reserves to establish the centre.
“However, we have been unable to generate a sustainable level of interest and unfortunately, we have concluded that we can no longer continue to subsidise the centre and have taken the difficult decision to discontinue the service.
“The last day of operation of the centre will be the 19th December 2019 and as a gesture of goodwill and to thank our customers for their support, access to the centre during this period is free of charge.
“We are all deeply disappointed that we are unable to continue to provide our service in Sheffield and I would like to assure you that this has been a very difficult decision which we have not taken lightly.”