The child is reported to be in a stable condition at the Colonial War Memorial Hospital in Suva.
The Health Ministry says the outbreak response teams are conducting investigations in the respective locations with quarantine and vaccination of contacts and at risk communities as appropriate.
Twelve cases are from the Serua/Namosi Subdivision in Wailali, Wainadoi, Navunikabi and Makosoi in Deuba.
Four cases are from Suva Subdivision in Samabula, Vatuwaqa, Tacirua and Wailekutu.
Three cases are from Rewa Subdivision in Koronivia, Nasilai Village Nakelo and Davuilevu.
The Health Ministry says measles is a highly contagious disease; therefore, non-essential travel to Saumakia Settlement in Naitasiri, Serua/Namosi, and Nasilai Village in Nakelo is strongly discouraged.