The hospital board has been reviewing the service as it battles to balance its books.
Medical director Dr Ashok Bhalla said they recognised that patients might be concerned as the NHS works out how to fill the gap left by the shutdown.
"I can reassure people that RNHRD will be doing all we can to support our existing patients, our staff and the commissioners who will now be working to identify where services can be reprovided.
"The Min provides a national neuro rehabilitation service and takes patients from right across the area.
"People may not realise that the numbers of local patients we care for are really quite small at around 20 people a year.
"The NHS will continue to provide high quality neurological rehabilitation services for those who need them. Current patients will continue to receive all the care and support they need while new arrangements are explored."
The NHS's South West Specialised Commissioning Team and NHS B&NES and Wiltshire will now work together to identify and consult on options for how the service can be reprovided.
Views of patients and carers will be taken into account as part of the consultation process.
The service will be stopped from March 31 next year.