The latest new cases were reported in France, Italy and Sweden.
It follows the confirmation of cases in the US, Spain and Portugal on Wednesday, as well as the investigation of 13 suspected cases in Canada.
Monkeypox is most common in remote parts of Central and West Africa.
Cases of the disease outside of the region are often linked to travel to the area.
Monkeypox is a rare viral infection which is usually mild and from which most people recover in a few weeks, according to the UK's National Health Service.
The virus does not spread easily between people and the risk to the wider public is said to be very low.
The first case of the disease in the UK was reported on 7 May. The patient had recently travelled to Nigeria, where they are believed to have caught the virus before travelling to England, the UK Health Security Agency said.
There are now nine confirmed cases in the UK. The source of these infections has not yet been confirmed but cases seem to have been "locally acquired", the World Health Organisation (WHO) says.
In Europe, one confirmed case was reported in Sweden on Thursday, as well as one in Italy and a suspected case in France. Swedish authorities said they were not sure how the individual had contracted the virus, but local media report that the individual in Italy had recently returned from the Canary Islands.
Five confirmed cases were also reported in Portugal on Wednesday, as well as seven in Spain.
Though no vaccine has been approved for Monkeypox in Europe, Spanish health authorities have reportedly purchased thousands of smallpox vaccines to deal with the outbreak, according to Spanish newspaper El País. Monkeypox is a member of the same family of viruses as smallpox.
In North America, health authorities in the US state of Massachusetts also confirmed that a man has been infected with Monkeypox.
He had recently travelled to Canada, where local media report that 13 suspected cases of the virus are being investigated.
According to health officials, the man has been hospitalised, is in "good condition" and "poses no risk to the public".