The deaths at Lochduhar, off Hardthorn Road, both occurred within 28 days of a postive test.
Meanwhile, a total of ten cases have now been recorded among staff and residents.
As a result, admissions and transfers have all been suspended and a multi-disciplinary team is providing support to the care home
Health officials say that as soon as the outbreak developed, immediate action was taken around implementing a number of additional robust infection control measures including increased testing and an enhanced decontamination schedule.
A spokesman for Dumfries and Galloway Health and Social Care Partnership said: “The operator of this care home has been faced with a challenging and difficult situation, but full credit is due to them and their very dedicated staff for the responses that have been mounted.
“Covid-19 is very highly infectious, which means that containing its spread is not easy – even when it is being met with all the correct protocols, including regular testing and vaccinations.”