Holiday spots that have been identified as a “moderate” risk include France, Italy, Spain, Croatia, Greece, Turkey and Switzerland.
If the virus spreads to France, there could be implications for the Euro 2016 championships, which begins on June 10.
Health officials are considering the impact of the virus in Brazil, ahead of the 2016 Olympic and Paralympic Games in Rio de Janeiro.
Last week, the World Health Organisation (WHO) urged pregnant women not to travel to the area and issued advice for athletes and visitors.
A third of countries in Europe, and surrounding regions, have a “moderate” risk of a Zika outbreak, according to the latest WHO risk assessment.
While the UK is deemed to be “low” risk, global health chiefs have urged preparedness. Officials should continue to be alert to cases early detection, and should provide public health advice to travellers, WHO said.
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.
Thirty-six countries — or 66% — have a low, very low, or no likelihood, owing to the absence of Aedes mosquitoes.
European countries where there is a ‘moderate’ risk of Zika are: France, Italy, Malta, Croatia, Israel, Spain Monaco, San Marino, Turkey, Greece, Switzerland, Bulgaria, Romania, Slovenia, Georgia, Albania, Bosnia and Herzegovina, and Montenegro
Geographical areas within Europe where there is a ‘high’ risk of Zika: Madeira Island, in Portugal, and the northeastern Black Sea Coast