It is understood the resident who is being cared for at the nursing home was released from hospital before showing signs of Covid-19.
The council-run complex has undergone a clean and the NHS Ayrshire & Arran public health team have been advising the home on infection control since the case emerged.
The top floor of the Racecourse Road building, which was previously unused, has just been opened to create greater distance between residents.
A council spokesman said: “We have opened up the top floor at South Lodge Care Home, so we can continue to accept people who have been discharged from hospital.
“Using this additional space, makes it easier to monitor new arrivals, to ensure they don’t show any symptoms of the coronavirus (COVID-19).”
Four people have died after an outbreak at the Glenfairn Care Home, which is also on Racecourse Road.
Tragically another 20 people with coronavirus have died in Prestwick's Berelands Care Home, which is privately run.
A council statement said: “We would like to reassure care home residents and their families that every measure is being taken to protect residents and staff and to prevent the spread of the virus.”
.Councillor Brian McGinley, chairman of the South Ayrshire Integration Joint Board said: “ I am standing in solidarity with all of those who are suffering from effects of the coronavirus at this time.
“I would like to extend my deepest sympathises to those who have lost loved ones.
“I wish to express my sincere gratitude to all the carers on the frontline for their dedication and commitment to helping those most in need.
“I am heartened to learn from public health that our care homes have developed a very positive approach to infection control and protecting our vulnerable residents.”
Councillor Julie Dettbarn, Adult Heath and Social Care Portfolio Holder for South Ayrshire Council said: “I would like to send my deepest condolences to the families of those who have sadly died.
"The coronavirus is hitting every part of society and we are doing everything we can to protect the vulnerable. Care homes are being supported, and I would like to recognise care home staff, who are going above and beyond under very challenging circumstances.”
The council said it could not name the care homes impacted by coronavirus as the information is held by the Scottish Government.
