Reports have named the schoolgirl as Imani Green, who was killed in the town of Duncans on Friday night.
Imani, from Balham, south London, is understood to have died after being shot twice, including once in the head, in what may have been a revenge attack, reports suggested. She arrived on the island with her mother shortly before New Year.
The young girl was said to have been with relatives at a cafe owned by her cousin when a gunman entered and opened fire.
Three others were injured in the shooting and taken to hospital for treatment, but are thought to be in a stable condition.