Boca Juniors ace Fabra suffered the injury in training for Colombia and Farid Diaz of Olimpia has been called up in his place.
Premier League side Everton are also potentially affected, with Fabra recently linked with a transfer to Goodison Park.
Boca reportedly wanted £7.5 million for the defender, making Fabra a potential bargain for Everton, especially if he proved himself a success at this summer's World Cup.
He is now out of his country's plans and will not travel to Russia.
His chances of a move to Everton this summer are now also over, and he faces a battle simply to play again in 2018.