The infection, which causes symptoms including mild fever, conjunctivitis and headache, has already been found in 21 countries in the Caribbean, North and South America.
It has been linked to thousands of babies being born with underdeveloped brains and some countries have advised women not to get pregnant.
No treatment or vaccine is available.
The virus was first detected in 1947 in monkeys in Africa. There have since been small, short-lived outbreaks in people on the continent, parts of Asia and in the Pacific Islands.
But it has spread on a massive scale in the Americas, where transmission was first detected in Brazil in May 2015.
Large numbers of the mosquitoes which carry the virus and a lack of any natural immunity is thought to be helping the infection to spread rapidly.