In a statement, Professor Chris Whitty said two members of the same family had tested positive for coronavirus.
The professor said: "The patients are receiving specialist NHS care, and we are using tried and tested infection control procedures to prevent further spread of the virus.
"The NHS is extremely well-prepared and used to managing infections and we are already working rapidly to identify any contacts the patients had, to prevent further spread.
"We have been preparing for UK cases of novel coronavirus and we have robust infection control measures in place to respond immediately.
"We are continuing to work closely with the World Health Organization and the international community as the outbreak in China develops to ensure we are ready for all eventualities."
The development came amid reports Virgin Atlantic has suspended its flights between Britain and China due to fears about the spread of the coronavirus.
The airline said in a statement it would suspend its daily operations between the UK and Shanghai for two weeks from Saturday.
The decision came after the World Health Organisation on Thursday declared the coronavirus outbreak an international public health emergency.
It also follows British Airways' decision to suspend flights to and from China, which is in place until at least Monday.
An aircraft carrying 110 passengers, including 83 Britons, has left Wuhan for the UK following the coronavirus outbreak in the Chinese city, the Foreign and Commonwealth Office (FCO) has said.
The plane, chartered by the FCO, landed at the Brize Norton RAF base in Oxfordshire at around 1pm.
It is understood the British passengers will be taken to an NHS facility on the Wirral to be quarantined for 14 days.
"It's welcome news that our evacuation flight has now left Wuhan," Foreign Secretary Dominic Raab said in a statement.
"We know how distressing the situation has been for those waiting to leave. We have been working round the clock to clear the way for a safe departure. The welfare of those trapped and public safety have been our overriding priorities."
After landing at Brize Norton, the chartered aircraft will continue to Spain, where the 27 non-British nationals on board will be processed by their EU home governments, the FCO said.