The resident lives at Scarborough Hall Care Home on Mount View Avenue.
A spokesman for Barchester Healthcare - which runs the home - said: “We can confirm that we have had a positive test result for COVID-19.
"We are confident in the processes in our home with all of our staff trained in infection control, and our staff have been brilliant in implementing this.
"We are following medical advice, and if and when needed we have sufficient and appropriate personal protection equipment.
"Please be reassured that our staff are trained in this practice, and we are confident that the right procedures will be followed to keep everyone as safe and well as possible.”
The home offers 24-hour residential and respite support to older people, in addition to care to people living with dementia.