Chief Medical Officer Dr Frank Atherton said the adult patient had returned from northern Italy, where the virus was contracted.
Swansea council leader Rob Stewart said the diagnosis had a link to the city’s Bishop Gore School, but there are no cases within any schools.
On Friday, a man on the Diamond Princess cruise ship became the first Briton to die of coronavirus.
Nineteen people have tested positive in the UK since the virus outbreak began in China.
There was one case in Northern Ireland on Thursday and two new cases in England on Friday.
Dr Atherton said the development was “not unexpected” and the patient was being treated at one of the four specialist units in England.Coronavirus in Wales: Questions and answers
He said it was “inevitable” there would be more cases.
Dr Atherton said: “Our job is to prepare for a significant number of cases, for an epidemic in the UK, or a pandemic if it becomes a global issue.”
He said the Welsh patient had been tested on Thursday, adding: “They developed symptoms and contacted the NHS and were assessed by colleagues from Public Health Wales.”
He said: “All appropriate measures to provide care for the individual and to reduce the risk of transmission to others are being taken.
“I’d like to take this opportunity to assure the public that Wales and the whole of the UK is well prepared for these types of incidents.”
He said to protect the patient’s confidentiality no further details regarding the individual would be released.
Experts have warned of school closures and the cancellation of major sporting events, concerts and festivals in the UK in a bid to stop the spread of the virus.
England’s chief medical officer, Prof Chris Whitty, said transmission of the virus between people in the UK was “just a matter of time”.
He said if the outbreak intensifies, it may be necessary to close schools and stop mass gatherings of people for “quite a long period of time, probably more than two months”.
The World Health Organization also warned that the outbreak had reached a “decisive point” and had “pandemic potential”.