The Zika virus is expected to spread to parts of Europe in late spring and summer, health leaders have said.
The news will come as a blow to some holidaymakers, particularly those who are pregnant or planning a pregnancy.
A third of countries in Europe have a "moderate" risk of a Zika outbreak, the World Health Organisation (WHO) said.
While the UK is deemed to be "low" risk, global health chiefs have urged preparedness. Officials should continue to be alert to detect imported cases early and provide public health advice to travellers, the WHO said.
A new risk assessment issued by the organisation's regional office says the overall risk across Europe is said to be "low to moderate".
The WHO said risk varies across the continent and is higher where the mosquito that carries the virus is present.
The likelihood of local Zika virus transmission, if no measures are taken to mitigate the threat, is moderate in 18 countries in Europe.
The risk is high on the island of Madeira and the north-eastern coast of the Black Sea.
Thirty-six countries - or 66% - have a low, very low or no likelihood, owing to the absence of Aedes mosquitoes or suitable climatic conditions for their establishment.
Dr Zsuzsanna Jakab, WHO regional director for Europe, said: "The new evidence published today tells us that there is a risk of spread of Zika virus disease in the European region and that this risk varies from country to country.
"With this risk assessment, we at WHO want to inform and target preparedness work in each European country based on its level of risk. We call particularly on countries at higher risk to strengthen their national capacities and prioritise the activities that will prevent a large Zika outbreak."
Dr Nedret Emiroglu, director of the Communicable Diseases and Health Security Division of the WHO's Regional Office for Europe, said: "We stand ready to support European countries on the ground in case of Zika virus outbreaks.
"Our support to countries in the region to prepare for and respond to health risks such as Zika is a key aspect of the reform of WHO's work in emergencies."
Mosquito-borne transmission of the virus is present in 58 countries, the organisation said.
The most recent figures show that 23 UK travellers have been infected after visiting affected regions.
The majority of those infected with Zika will have no symptoms but for others it can cause a mild illness with symptoms including a rash, fever and headache.
Serious complications that arise from infection are not common but experts have said the virus can cause microcephaly and other congenital abnormalities as well as a rare disorder called Guillain-Barre syndrome.