Tavon Kaiseen Alleyne, 21, was walking in the St Michael's area near his home around 7 pm on December 26 when he was shot at by an unidentified man several times, Sky News reported.
Alleyne was rushed to the hospital in a private vehicle but he succumbed to his injuries.
The police has launched an investigation into the case. Rihanna, 29, took to Instagram to mourn her cousin's demise, while calling for the elimination of gun violence.
"RIP cousin... Can't believe it was just last night that I held you in my arms! Never thought that would be the last time I felt the warmth in your body! Love you always man! End Gun Violence," the Grammy winner wrote, alongside her picture with Alleyne.