Jack, 31 had been brought in on trial to cover for the injury of Heinz Muller. Jack has already played for British clubs Reading, Dundee and Gillingham started out in his homeland with Docs Khelwaalas, W Connection and San Juan Jabloteh.
Jack also played for Trinidad & Tobago at the 2006 World Cup in Germany.
Reds boss Simon Davey said:
"I can confirm that Kelvin has been with us for the last week on trial and, unfortunately, has today broken his leg in a freak training ground accident.
"Everybody at Barnsley Football Club wishes Kelvin a very speedy recovery"