On Monday, the Health Protection Agency (HPA) said one person who had recently travelled to the Middle East and Pakistan was being treated in an intensive care unit at a Manchester hospital after becoming infected with a new type of coronavirus.
Two days later, a relative of the patient who had no recent travel history became infected and now the HPA has said a third person, who has also not travelled recently, is infected.
But the HPA said the risk associated with novel coronavirus to the UK population remained low.
The newest patient is recovering from a mild respiratory illness and is currently well. This latest case brings the total number of confirmed cases globally to 12, of which four have been diagnosed in the UK.
The second family member has an existing medical condition that might have made them more susceptible to respiratory infections, the HPA said on Wednesday.
Professor John Watson, head of the respiratory diseases department at the HPA, said: "Although this (third) patient had a mild form of respiratory illness, as a precaution the HPA is advising that the patient self-isolate and limit contact with non-household members."
Five patients have died as a result of the infectious disease, none in the UK.