Franjic rolled his ankle in Roar's 2-1 win over Adelaide United on Sunday and will miss at least one week with a low-grade strain.
It's a blow for Brisbane as the utility, who played right full-back in the Socceroos' 4-3 loss to Ecuador last week, has been among Roar's most influential and consistent players all season.
Regular defensive back-up James Donaghie is also currently sidelined, meaning Jack Hingert is likely to return to the Roar's defence for the match at Allianz Stadium.
Central defender Jade North was also replaced in the second half against Adelaide with hamstring tightness, but Brisbane coach Mike Mulvey has little concern about the veteran playing the fourth-placed Sky Blues.
Roar holds a 10-point lead over second-placed Western Sydney Wanderers with five rounds reamining.