The Rainbow Day Centre, based in Carnwadric Church in Thornliebank, is used by around 22 elderly people a day.
Many of the service users live alone and have no family nearby to help them, so the centre provides the chance to socialise instead of spending days indoors.
Around 20 of the attendees have received letters from the council telling them they will have to pay up to £15 a day for centre charges.
So far, only four members have been told they can use the facilities for free.
Ann Walsh, senior care officer at the centre, said: "At the moment we've had two people pull out due to the threat of the charges.
"I went to do a referral yesterday.
"I started to explain about the charges through the city council.
"Right away he said no, he wouldn't attend and that's what we are up against.
"When you bring new referrals in and tell them about the charges, you are scaring them."
Yesterday, Ann was also informed by the council that members would have to pay for the five annual trips they go on per year, on top of the existing £20 they pay to the centre for their accommodation and travel on the outings.
"It's not going to be feasible." Anne said.
"It means we are going to have to cancel the outings."
Margaret Stobbart, 65, lives on her own and comes to the centre twice a week.
She is concerned about the amount she may have to pay to attend, and said: "I'm paying £108 for Cordia to come three times a week to help me use the shower and I pay for my mobility scooter as well, so I don't know how I will afford any extra."
Another service user, Milly Love, has been hit with the maximum charge of £15 per day.
The 93-year-old said: "The council say they are caring for their senior citizens, but where? I have to pay £45 for the week, but if I didn't come here I'd vegetate."
Phyllis Ferns, 55, from Carnwadric, is a full-time carer for her mum Georgina who uses the centre and is "absolutely disgusted" with the impending charges.
Phyllis said: "These are elderly people who have worked for their whole lives and that's a lot of money to be paying out.
"My mum has to pay £45 a week but she already said to me that if she has to pay it then she's not going."
James Dornan, Cathcart SNP MSP said: "People will not be able to pay the charges which will then have a negative impact on their health.
"This decision has been taken from an income- generating perspective with no consideration for the wellbeing of the elderly people who use the service.
"At the least the implementation should be delayed until the practical difficulties for users and service providers can be sorted out."
A spokesman for Glasgow City Council said: "Many other local authorities charge for day services and in Glasgow the charge is based on the ability to pay.
"So far just two people out of the 913 who use council-run day care have dropped out because of the charge while up to 50% of service users are not being charged anything at all.
"Asking older people to make a contribution to the cost of their day care services is about being consistent and fair to all social work users.
"Anyone who stops using a day centre will have their needs reassessed to ensure they receive appropriate support."