Public Health Wales (PHW) said the people were infected abroad and the two patients are from the same household.
Both PHW and Public Health England are monitoring the cases, which has seen the two people admitted to hospital in England.
One patient has since been released.
“Confirmed cases of monkeypox are a rare event in the UK, and the risk to the general public is very low,” said Richard Firth, PHW’s consultant in health protection.
“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.
