The risk to the wider public is considered to be very low, PHE said.
The Nigerian naval officer began to develop symptoms of the virus, which has a mortality rate of between one and ten per cent, while on the British base.
On Friday after his diagnosis was confirmed the patient was moved to the infectious disease unit at the Royal Free Hospital in London. He was said to be in a stable condition.
Monkeypox is a rare viral infection, similar to smallpox but not as deadly. It is usually mild and self-limiting with most people recovering within a few weeks, but severe illness and death can occur.