Belleisle House, in Govanhill, run by the Dixon Community charity for 21 years, will shut its doors in less than two months.
The home has been running at a £70,000 deficit for months because the charity has been unable to fill three of the 10 rooms.
Two weeks ago Belleisle, which has a staff of 18, was given three six-star ratings by the Care Inspectorate, the highest that can be awarded.
Some relatives were in tears as they were given the news at a meeting last Thursday night.
They have warned that some of the most vulnerable residents, aged up to 97, will not survive a relocation and have launched a Facebook campaign to keep the home open.
The charity said efforts to fill the empty rooms had been unsuccessful because families were looking for more modern homes, with en-suite facilties.
Chairman George Patterson said the problem had been exacerbated by the opening of a number of new homes in Glasgow.
However, relatives of the home's seven elderly residents are angry they were given little warning about the group's financial problems.
Alison Bigrigg, a doctor from Pollokshields, whose mother Doreen, 83, is in the home, said: "After no consultation with carers it was announced the unit would close in the next three months.
"The only reason given by social services was that the unit had incurred a small financial loss.
"They accept it gives excellent care and is better than many units in the city."
"I do feel Dixon are handling the process badly."
Margaret McGowan's 87-year-old mother mother, Jean Young, has been cared for in the home for a year and a half.
Margaret, 58, from Bearsden, said: "I'm absolutely distraught. I can't praise the staff enough.
"It's a unique home. It is small and as soon as you walk in you feel how welcoming it is."
Collette Tracey, from Kings Park, whose mother Betty Phillips, 82, is in the home, said: "I don't know what we are going to do.
"I don't think she will cope in another institution.
"Apparently they knew in February but didn't let people know."
Mr Patterson said: "We have basically run out of money. We have had three months of no referrals.
"We have been trying to resolve this situation for months.
"It is very, very sad, but you have to be realistic.
"There has been a number of new homes opening. We have two people in recently but they wanted en-suite facilities.
"Unfortunately a lot of people don't always look at the care that is being provided as the most important factor."
The charity said it was hopeful some of the 18 staff would be relocated to council and privately-run homes.