Franjic underwent scans on his right hamstring on Saturday and they confirmed that he has torn the muscle, which will rule the right-back out of the rest of the tournament.
Australia coach Ange Postecoglou was gutted about the injury - for Franjic, but also for the team after the right-back's strong first half in Cuiaba.
"Ivan's no good, he had a scan today and has a fairly significant hamstring tear. That rules him out for the tournament, and that's a real disappointment," Postecoglou told reporters.
"He was growing into the tournament and into the game; the first 15 minutes everything was a bit quick for him but after that he settled into the task and set up the goal really well.
"He was getting to grips with it so it's a massive disappointment. I'll talk to him later but there's not a lot you can say. But what's tasted should be motivation to come back for more."
Franjic injured his hamstring in the opening minutes of the second half versus Chile on Friday when he leapt for a high ball.
The Brisbane Roar defender had created Australia's goal in the 3-1 loss to Chile, crossing for Tim Cahill to score.