Jedinak is still struggling with a groin injury, while Trent Sainsbury has been retained despite a lack of club football in China.
Nikita Rukavytsya, Aziz Behich, Craig Goodwin, Josh Risdon and Matthew Jurman return to the squad with Jamie Maclaren, Alex Gersbach and Ryan McGowan among the notable absentees.
Wildcard Nikita Rukavytsya, who plays his club football with Israeli side Maccabi Haifa, is perhaps the biggest surprise.
The 30-year-old comes in from the cold for the two-legged playoff, making his first squad under Postecoglou.
His last appearance for the national team was in the 3-0 friendly win over Canada in 2013 under caretaker coach Aurelio Vidmar, in the wake of Holger Osieck's sacking.
Wide players Risdon and Goodwin return to the national team setup for the first time since last November's away trip to Thailand.
Jurman, who has been named ahead of Asian Cup winner Matthew Spiranovic, has the chance to win his first Socceroos cap.
Gersbach, who impressed in the last qualifier, missed out in favour of Behich due to a lack of game time at his club Rosenborg and because of a light injury concern, Postecoglou confirmed.
"I just felt he hadn't had a lot of football coming into the last camp and with a slight niggle he was at best going to get one game in this weekend," he said.
"So with Aziz going really well in Turkey, I just felt his experience would be needed."
Postecoglou said he was "overall pretty pleased" with the squad, spearheaded by PFA player of the year Aaron Mooy, Bundesliga sharpshooter Mathew Leckie and Celtic's Tom Rogic.
"Jedinak couldn't come up for this game but the rest of the squad is coming into camp hopefully after this weekend's games in good health, in good form and looking forward to the challenge," Postecoglou said.
Jedinak's unavailability is Australia's biggest concern.
The Aston Villa midfielder has struggled with the groin issue that ruled him out of the Confederations Cup for months.
He has managed just 46 minutes of football this season for his Championship side and was unused in their three wins during the past week.
"He had a run of 45 minutes (earlier this month) and he didn't pull up well and that gave me the inkling he was unlikely," Postecoglou said.
"We always want to give him every opportunity. He's very keen to be involved ... he's certainly confident he'll be back soon."
Awer Mabil has also dropped out from the squad that produced a 2-0 loss in Japan and 2-1 home defeat of Thailand last month.
Australia must beat Syria over two legs - in Malaysia on October 5 before hosting them in Sydney on October 10.
Should they progress, they'll face a final home-and-away playoff against the fourth-placed CONCACAF side in November to book a spot at next year's World Cup in Russia.
With sluggish ticket sales for the home tie at ANZ Stadium against Syria on October 10, Postecoglou called upon Sydney-based fans to back his side.
"It is important for us to have a large and vocal home crowd for the second match of this series, and I'm sure the boys will appreciate all the support from the local fans," he said.
Mark Milligan will wear the captain's armband in place of Jedinak, as he did against Thailand earlier this month.
SOCCEROOS SQUAD FOR WORLD CUP PLAYOFF WITH SYRIA
GOALKEEPERS: Mat Ryan, Mitchell Langerak, Danny Vukovic
DEFENDERS: Aziz Behich, Milos Degenek, Mathew Jurman, Josh Risdon, Trent Sainsbury, Brad Smith, Bailey Wright
MIDFIELDERS: Mustafa Amini, Craig Goodwin, Jackson Irvine, Massimo Luongo, Mark Milligan, Aaron Mooy, Tom Rogic, James Troisi
FORWARDS: Tim Cahill, Tomi Juric, Robbie Kruse, Mathew Leckie, Nikita Rukavytsya