The midfielder was named in the preliminary 30-player list for the matches, but has been deemed unfit to take part because of a groin injury - the same ailment that ruled the 33-year-old out of the Confederations Cup.
Coach Ange Postecoglou made the decision despite the knowledge Jedinak is likely to return to the field with Championship side Aston Villa this weekend.
"We wanted to give Mile every chance. He was very keen. But speaking to him last night, (he’s) not going to get in a game to see how he feels," Postecoglou said at the squad's unveiling.
"Being a long trip, and his long absence from game time, he felt he wasn’t right so he ruled himself out.
“I think it would’ve been great to have him there, he’s the captain and been a big part of what we’ve done over the last four years.
"He’s been struggling with this injury for quite a while but kept playing with us through that.
"We have enough depth in that area to cover his absence."
Sydney FC goalkeeper Danny Vukovic and Pacos Ferreira winger Awer Mabil are the only uncapped players in the squad, while Matthew Spiranovic has been selected for the first time since being omitted in March.
Fellow defender Trent Sainsbury has been picked despite having not played any football since the Confederations Cup because of a groin injury.
The seven players to cut from the initial 30-man party along with Jedinak include Aziz Behich, Adam Federici, Ajdin Hrustic, James Jeggo, Riley McGree and Matthew Jurman.
Goalkeepers: Mitchell Langerak, Mathew Ryan, Daniel Vukovic
Defence: Milos Degenek, Alex Gersbach, Ryan McGowan, Trent Sainsbury, Brad Smith, Matthew Spiranovic, Bailey Wright
Midfield: Mustafa Amini, Jackson Irvine, Massimo Luongo, Mark Milligan, Aaron Mooy, Tom Rogic, James Troisi
Forwards: Tim Cahill, Tomi Juric, Robbie Kruse, Mathew Leckie, Awer Mabil, Jamie Maclaren