A spokesman for Public Health Wales said the index case was acquired overseas and the two patients are members of the same household.
Richard Firth, consultant in health protection at Public Health Wales, said: “Confirmed cases of monkeypox are a rare event in the UK, and the risk to the general public is very low.
“We have worked with multi agency colleagues, following tried and tested protocols and procedures, and identified all close contacts.
“Actions have been put in place to minimise the likelihood of further infection.
“Monkeypox is a rare disease caused by the monkeypox virus and has been reported mainly in central and West African countries.
“Monkeypox, in most cases, is a mild condition which will resolve on its own and have no long-term effects on a person’s health. Most people recover within a few weeks.”
Symptoms include fever, headaches, swellings, back pain, aching muscles and a general listlessness.
After the fever, a rash can develop, often beginning on the face then spreading to other parts of the body.
The rash can be extremely itchy, changes and goes through different stages before finally forming a scab, which later falls off - which can cause scarring.
The infection usually clears up on its own and lasts between 14 and 21 days.
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