Dr Frank Atherton, Wales's chief medical officer, said: "I can confirm that one patient in Wales has tested positive for coronavirus (COVID-19).
"All appropriate measures to provide care for the individual and to reduce the risk of transmission to others are being taken."
Dr Atherton added that the patient had recently returned to Wales from northern Italy, where they contracted the illness.
Dr Giri Shankar, incident director for the Covid-19 outbreak response at Public Health Wales, said: "Public Health Wales is working hard to identify close contacts, and we are taking all appropriate actions to reduce any risk to the public's health."
Dr Shankar claimed that Wales and the UK as a whole were "well prepared for these types of incidents".
The health ministry confirmed that there are now 19 UK coronavirus cases, with 17 in England, one in Northern Ireland and one in Wales.
This total includes two new cases in England which were recently confirmed by the Department of Health.
Concerning these two patients, Professor Chris Whitty, England's chief medical officer, said: "The virus was passed on in Iran and the patients have been transferred to specialist NHS infection centres at the Royal Free Hospital."
The first confirmed case in the UK was on January 31.
On Friday, a World Health Organization (WHO) spokesman said that the outbreak is "getting bigger", with the possibility that it will reach further countries, "if not all countries".
These comments come as the first case in sub-Saharan Africa was confirmed in Nigeria on Friday.
The patient is an Italian man who flew to Nigeria from Milan on February 24, but did not show symptoms when the plane landed.
Nigerian authorities are in the process of observing passengers who were on the same plane as the patient, and are trying to identify the people he came into contact with in Lagos.
The virus, which was first identified in China in December last year, has so far killed almost 2,800 people in mainland China and about 70 people in other countries and territories.
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