Agnès Buzyn, the French health minister, last year made vaccinations against measles and 11 other diseases compulsory for children.
Buzyn has made extending vaccination coverage one of her top priorities
Measles caused 110,000 deaths worldwide in 2017, the WHO said, despite the widespread availability of a vaccine. The majority of those who died were children under five.
The Costa Rica Star reported that neither the boy nor his mother, 30, had been vaccinated.
The father, 35, is reportedly not up to date with his vaccinations. The newspaper said the parents told a doctor in Costa Rica that other children at the boy's school in France had contracted measles.
A spokeswoman for the French health ministry confirmed that a French 5-year-old boy in Costa Rica was suffering from measles.
She said the measles vaccination had only been compulsory in France for children born on or after 1 January 2018, and the boy affected was therefore not covered by the requirement introduced by the current government
Costa Rican authorities said they had informed their French counterparts so that they can track whether others in France have been infected.
Costa Rica has not had a domestic measles case since 2006. The last recorded case brought in from another country was in 2014.
The boy is being treated and both he and his parents will be held in quarantine for at least seven days at the Monseñor Sanabria Hospital in the port town of Puntarenas, near the Santa Teresa beach resort where they were staying. The family arrived in Costa Rica on 18 February.
The Costa Rican health authorities are trying to establish who may have come into contact with the boy at the resort, on his flight, or at a hotel in the capital, San José, where the family spent one night.
The Costa Rican health ministry said 26 people known to have had contact with family have now been vaccinated. In a statement, the ministry said: "Our country enjoys very good vaccination coverage in general. However, in order to avoid particular cases and their possible complications, it is important that those in charge of minors ensure that children have the complete vaccination scheme."
In Britain, a paper published by a doctor in 1998 linking autism with the MMR vaccine (measles, mumps and rubella) raised anxiety about the jab.
The doctor, Andrew Wakefield, was struck off the UK medical register in 2010 for dishonesty and failing to act in the best interests of child patients.
This article originally appeared on the Daily Telegraph.