Barrett's mother Kesha Duhaney is a native of Brooklyn, New York. She was a nationally ranked sprinter and long jumper for St. John's University before working for the Canadian Imperial Bank of Commerce. Barrett's parents first met while attending St. John's. His maternal aunt Dahlia Duhaney was a member of the Jamaica team 4 × 100 m relay that won a gold medal at the 1991 IAAF World Championships. Also on his mother's side, his grandparents ran track for the Jamaica national team, and his uncle played football for the University of Maryland.