Cartlidge House, in Oakengates, is run by Accord Housing Association, which says staff are continuing to provide the best possible care for all its residents.
Michelle Barker, head of residential and nursing care services at Accord, said: "As is the case in many care homes across the country, indeed across the world, we do have some customers showing possible symptoms of coronavirus, and our excellent team of carers is continuing to provide the best possible care for them, following all Public Health England guidance.
"As per Government policy, members of our staff have not received testing, a few of our residents that are showing symptoms have been tested, but not all."
She said the residential home has an "excellent relationship" with its local GP practice.
"They have always been very supportive to our staff and our customers, and this support has continued over the last few weeks, and we are very grateful for their commitment and support," she added.
"Nationally, everyone in health care is working during some very difficult times at the moment, but we are continuing to work closely together, supporting each other.
"Maintaining contact with relatives is also our priority and we are maintaining an ongoing dialogue with them.”