One of the patients is currently being treated at the specialist High Consequence Infectious Diseases Unit at Royal Liverpool Hospital.
Public Health Wales and Public Health England were monitoring the two Welsh cases on Thursday, which saw the two patients admitted to a hospital in England, with one since released.
A small number of cases had previously been identified in Lancashire in 2018.
Here is everything you need to know about the viral infection.
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What is monkeypox?
A rare disease caused by a viral infection.
How does it spread?
Most commonly when a person comes into close contact with an infected animal. It is not spread easily between people.
What are the symptoms?
Infected people usually start to show symptoms between five and 21 days after infection.
These include fever, headache, muscle aches, backache, swollen lymph nodes, chills and exhaustion.
How serious is it?
Most patients recover within a few weeks and do not need treatment, but it can cause severe illness in some people.
Why is it called monkeypox?
The disease was first discovered in monkeys kept for research in 1958.
The first human case was recorded in 1970 in the Democratic Republic of Congo.
Where is it prevalent?
Cases have been reported in a number of countries in Africa, including Cameroon, the Central African Republic, the Democratic Republic of Congo, Liberia and Nigeria.
An outbreak occurred in America in 2003 after rodents were imported from Africa.
There was a sustained outbreak in Nigeria in 2017 and there have been sporadic cases reported since then.