All medical staff and patients of the nursing home located in the Tallab Tillo area of the city are being tested for the disease as a precautionary measure, the officials said.
They said priority would be given to those who were in direct contact with the COVID-positive patient.
The building is being sanitised, and random sampling will be done before the nursing home is opened to the public again, the officials added.
Meanwhile, Arnia police station in the outskirts of Jammu was closed for visitors after an officer posted there tested positive for COVID-19, an official said.
This is the second police station in Jammu district to be declared "out of bounds" following detection of COVID cases.
On Sunday, Janipur police station in the city was closed after an officer tested positive for the disease there.
The staff posted at the Arnia police station are being tested. While 32 of them provided their samples on Monday morning, the rest will be tested on Tuesday, the official said.
He said a decision to reopen both the police stations would be taken after the test reports are received.
Jammu region has recorded 2,243 positive cases of COVID-19 till Sunday evening. While 17 of them have died, 1,473 patients have been cured.
While Jammu district accounted for 10 fatalities, two deaths were reported in Doda and one death each was registered in Udhampur, Rajouri, Samba, Poonch and Kathua.
A total of 488 cases of the infection were reported in Jammu, followed by 302 in Udhampur, 300 in Kathua, 275 in Rajouri, 261 in Ramban, 244 in Samba, 142 in Poonch, 128 in Doda, 57 in Reasi and 46 in Kishtwar. TAS AB IJT