The UK Health Security Agency (UKHSA) said the overall risk to the population “remains low”.
The patient is a household contact of the first UK case, which was detected in London at the end of last month.
The person is receiving specialist care at Guy’s and St Thomas’ NHS Foundation Trust in London.
According to UKHSA, they had been isolating since being identified as a contact of the first case, so no further contact tracing is required.
Professor Susan Hopkins, chief medical adviser at UKHSA, said: “Mpox is very infectious in households with close contact and so it is not unexpected to see further cases within the same household.
“The overall risk to the UK population remains low.”
The first UK case of Clade Ib mpox was contracted by a person who had been on holiday in Africa and travelled back to the UK on an overnight flight on October 21.
They developed flu-like symptoms more than 24 hours later and, on October 24, started to develop a rash which worsened.
Two more cases, also household contacts of the first patient, were announced on Monday, with the patients also getting specialist care at Guy’s and St Thomas’.
The World Health Organisation (WHO) said these are the first locally transmitted mpox Clade Ib cases in Europe, and the first outside of Africa since it declared a public health emergency of international concern because of the rapid spread of the strain in August.
Dr Hans Henri P Kluge, WHO’s regional director for Europe, said: “Local transmission of mpox Clade Ib should be the impetus for health systems to heighten surveillance measures and be prepared for rapid contact tracing of suspected and confirmed cases.”
Mpox spreads between people through direct contact with rash, skin lesions or scabs caused by the virus, including during sexual contact, kissing, cuddling or other skin-to-skin contact. There is also a risk from contact with bodily fluids.
A report from the WHO said there had been more than 40,000 mpox cases linked to almost 1,000 deaths in Africa as of the end of September.