The young girl was with relatives at a cafe owned by her cousin when a gunman entered and opened fire following an argument.
Three others were injured in the shooting and taken to hospital for treatment but are thought to be in a stable condition.
Deputy Superintendent Steve Brown from the Jamaican police said a “high level team” from Kingston is assisting with the inquiry: “They’re confident of getting a breakthrough very soon.
He said it was too early to know if Imani was the intended target: “What we do know is that they don’t normally target children in Jamaica. We’re not leaving anything to chance and not leaving any stone unturned. There will be an investigation and we will determine if she was the target.”
Imani arrived on the island with her mother shortly before New Year to stay with relatives.
The Foreign Office has confirmed the death of a British national in Jamaica on Friday 11 January and said it is providing consular assistance to the family.
Shadow justice secretary Sadiq Khan, MP for Tooting, said: “(I am) devastated to hear the news of eight-year-old schoolgirl Imani Green, a pupil at a Tooting primary school.