This has happened at Singleton Park in Courance near Lockerbie.
Last week admissions were suspended to the home after 10 people tested positive for the virus.
Today, Dumfries and Galloway Health and Social Care Partnership confirmed that one person had died within 28 days of testing positive for Covid-19.
A spokesman for Dumfries and Galloway Health and Social Care Partnership said: “This outbreak has resulted in a very dedicated response from staff, which is currently comprised of Singleton Park staff working alongside staff drawn from the Partnership.
“The outbreak demonstrates again how highly transmissible the Covid-19 virus is.
“Everyone should be conscious that Covid-19 can result in mild symptoms, and sometimes none at all. This can mask its spread to more vulnerable individuals where it can pose a very significant risk.
"Following the guidance around appropriate wearing of face coverings, hand hygiene, considering our social interactions, regular testing and getting vaccinated remain vital in reducing risk – but these are by no means an absolute guarantee of protection.