The 26-year-old picked up the problem on Friday during his country's 3-1 defeat to Chile.
Despite seeing his participation at the tournament come to an end, Franjic has wished his teammates the best of luck as they try to get out of Group B.
"You work so hard to get to a World Cup and 50 minutes into a World Cup, your dream is over," he is quoted as saying by FIFA.com. "It's disappointing but the boys have my full support and I'll be backing them 100% of the way."
The Aussies continue their campaign on Wednesday when they face group leaders the Netherlands.