The Boca Juniors defender underwent tests after sustaining an injury to his left knee at Colombia's training camp in Italy.
ACL damage was confirmed by the Colombian Football Federation (FCF), which is yet to name a replacement for Fabra in its 23-man squad.
"The Colombian team reports with regret that Frank Fabra suffered a rupture of the anterior cruciate ligament of the left knee," an FCF statement read. "After diagnostic tests of the defender [on Saturday], the medical team confirmed the injury that was expected.
"The entire squad, coaching team and staff received confirmation of the news with great pain."
Colomba drew 0-0 with Egypt in its only warm-up friendly before beginning its World Cup campaign against Japan, with Group H matches against Poland and Senegal to follow.