Professor Chris Whitty said the person, who did not contract the virus in the UK, is currently being transferred to one of the UK’s four infectious diseases centres for treatment.
Two other patients are still being treated at the Royal Victoria Infirmary infectious diseases centre in Newcastle upon Tyne.
In a statement, Prof Whitty said: “A further patient has tested positive for coronavirus, bringing the total number of cases in the UK to three.
“The individual did not acquire this in the UK.
“The patient is being transferred to a specialist NHS centre, and we are using robust infection control measures to prevent any possible further spread of the virus.
“The NHS is well prepared to manage these cases and we are now working quickly to identify any contacts the patient has had.”
It comes as the Chinese ambassador to the UK warned against “rumours and panic” over coronavirus.
Speaking to reporters in London, Liu Xiaoming called on the UK Government to support China in its handling of the coronavirus outbreak, but insisted that relations between Chinese president, Xi Jinping, and the UK Prime Minister were good.
He said: “It is of hope that governments of all countries, including the UK, should understand and support China’s efforts, avoid overreaction, avoid creating panic, and ensure normal co-operation and exchanges between countries.”
Earlier, Mr Liu tweeted that the UK should respect the World Health Organisation (WHO), which has warned against travel and trade restrictions on China.
The Foreign Office in the UK has advised Britons in China to leave if they are able to.
Mr Liu’s tweet said: “WHO has reiterated that it disapproves of and is even against overreaction to the epidemic, including travel and trade restrictions on China.
“We hope the UK will respect the professional advice of WHO and ensure the normal co-operation and exchanges between China and the UK.”
Meanwhile, a British man who is among 3,700 people being quarantined on a cruise ship in Japan has voiced concerns over ongoing monitoring for the disease on board and what his fate will be when he returns to the UK.
David Abel, of Northamptonshire, praised cruise line Princess Cruises for its handling of the situation so far, but said fears remain about efforts to fight the disease on the ship.
Health workers in the port city of Yokohama said on Thursday that 10 more people on the Diamond Princess had tested positive for the disease, in addition to 10 others on Wednesday when the ship was ordered to be isolated.