All of the deceased residents had underlying health conditions and their families have been made aware.Two staff members have tested positive and are being treated in hospital.
The care home said tests were not carried out on residents as they are only carried out when people are admitted to hospital.
A Four Seasons Health Care spokeswoman said: “With deep sadness we can confirm that 13 residents at Burlington Care Home have passed away over the past seven days.
“Our condolences are with their families and we are providing them with our ongoing support during this difficult time.
“The passing of a loved one is always traumatic irrespective of the circumstances.
“Within the home the focus of the team continues to be the ongoing care and protection of all our residents and our colleagues, two of whom are currently being treated for coronavirus.”Our strict protocols on infectious diseases are in place, including social distancing, and we are closely monitoring the health of the other residents and colleagues.
“In these exceptional circumstances we are sincerely grateful for the dedication of our colleagues and can assure our residents and their families that we are putting all our resources and energy into supporting and protecting everyone in our homes.”
The Care Inspectorate have been made aware of the deaths and are in contact with the care service, as well as the local health and social care partnership.
A spokesperson said: “We are aware of the tragic death of residents at this care home as a result of Covid-19.
“Our thoughts are with the loved ones of those affected as well as the the staff and wider community of the home.
“All of Scotland’s social care sector is working under very difficult circumstances to care for people during the pandemic and the Care Inspectorate is doing all it can to support them.”