The 5-year-old and his parents are on holidays in the Latin American country.
An unvaccinated 5-year-old French boy on holidays with his parents is suspected of having reintroduced measles to Costa Rica, the health ministry said.
The three tourists arrived in the Latin American country on February 18 and the boy has since been put under quarantine at a hospital in Puntarenas, a costal city in the north-east, the health ministry said in a statement.
The country's authorities have contacted France so they can check if other people were infected on their side.
Authorities are also looking for any people the young boy might have come into contact with since the family's arrival in Costa Rica, which had been measles-free since 2014.
The highly-infectious disease, which is most common in young children, leads to symptoms including a high fever and white spots inside the mouth before developing into the "measles rash".
The most serious complications from severe measles include blindness, encephalitis (an infection that causes brain swelling), diarrhoea and dehydration, and severe respiratory infections, according to WHO.
More than 82,000 people in Europe were infected with the measles in 2018, marking the highest number of cases reported in the region this decade, the World Health Organization (WHO) warned earlier this month.
Seventy-two children and adults died from the disease.
WHO said the historic annual figure was three times higher than that of 2017 and 15 times greater than the record low reported in 2016.
Ukraine recorded the highest number of measles cases in Europe in 2018, at 53,218.
France (2,913) and Italy (2,517) were also among the 10 most affected countries.