The Argentine attacker, who was signed as an injury replacement for Venezuela forward Vargas, has found himself on the sidelines for a chunk of the remaining regular season.
The timing couldnt be any worse for Ernie Merrick's side as they battle to lock down a top-two spot with only seven games remaining in the season.
Newcastle are five points clear of third placed Melbourne City and are in the box seat to claim a finals bye and a crucial home match in the second week of the A-League finals.
Like Vargas, Rodriguez has become a fan favourite among Newcastle fans despite only a short tenure at Macdonald Jones Stadium.
The injury opens the door for Riley McGree to start for the Jets against the Brisbane Roar at Suncorp Stadium on Saturday.