The 12-bed facility is to close until March as part of money-saving measures proposed by the Department of Health.
More than 4,000 people are affected by MS in Northern Ireland – the highest rates in the UK.
Philomena McKay from Cushendun says the centre is “an absolute lifeline”.
She added: “I suffer from MS but my family also suffer. You can go and stay there for two weeks’ respite and give your family a break.
“They have physio, dental and podiatry care there. Think of all the money they are saving by not having to pay for home visits. I have made so many friends there and the staff are excellent.”
Patricia Gordon, director of the MS Society in Northern Ireland, said: “Regular, appropriate breaks are crucial for maintaining the wellbeing of carers and people with MS. Inadequate respite provision can lead to declining health, increasing pressure on carers and unnecessary and costly hospital admissions.”
DUP MP for North Antrim Ian Paisley said the saving of closing the centre is “minuscule, merely £500,000, yet the impact is a major one”.
The closure is also opposed by Donal Cunningham, SDLP chairman of Moyle District Council, UUP MLA Robin Swann and Sinn Féin MLA Daithí McKay.
The Northern Health Trust said it must reduce spending by £6.9m for 2014/5. It will temporarily close 27 intermediate care/rehabilitation beds, including seven beds in the Mid Ulster Hospital and 20 beds in Dalriada Hospital.
“This will allow the trust to reduce bank and agency usage with staff being redeployed to support acute services at Causeway and Antrim Area hospitals,” the trust said. The length of stay in intermediate care beds has been reduced, allowing patients’ needs to be met with reduced bed numbers, it added.
It will “temporarily reprovide MS respite services currently provided in Dalriada Hospital in the independent sector, or through direct payments to service users, based on service user choice”.