The 29-year-old has only been a peripheral figure at The Hawthorns since arriving in the summer, making just five Championship appearances, four of which have come from the bench.
Rogic has only come up with one assist in that time, but he was still expected to earn a place on the plane for the Socceroos for the Qatar World Cup, having been a regular at the 2018 edition.
However, Arnold has taken the bold decision to leave the 53-cap international - who has not played for his country since February 1 - out of his 26-man squad.
Addressing the media after making his decisions, Arnold said of Rogic's omission: "At the end of the day I only can pick two players for every position. We've obviously gone for Ajdin Hrustic and Riley McGree and again we need some flexibility and players that are extremely fit and ready.
"Tommy's been absolutely brilliant for Australian football and he will continue to be so but I have to make those decisions."
Rogic is not the only notable omission from the Socceroos' squad, as experienced goalkeeper Mitchell Langerak has also been left out after earning a call-up for September's fixtures.
Arnold has favoured 75-cap skipper Mathew Ryan, Danny Vukovic and Andrew Redmayne in between the sticks, with the latter pair only making four appearances each for their country.
The Australia boss insisted that the decision to omit Langerak was down to goalkeeping coach John Crawley, adding: "Bringing Mitch back (for the New Zealand friendlies), it was about a plan in case something happened to one of the other goalkeepers and at the end of the day, and John Crawley's beliefs.
"We believe we've picked the three best goalkeepers for this World Cup and that's what we're sticking to."
Centre-back Trent Sainsbury - who plays his club football in Qatar for Al-Wakrah - will not be playing at the World Cup either, but there are still some familiar names in the squad.
Stoke City's Harry Souttar is part of the squad despite his injury woes, while captain Mathew Leckie will be appearing in his third World Cup for the Socceroos.
Scotland-based Aaron Mooy and Martin Boyle have also earned call-ups, as has 18-year-old attacking starlet Garang Kuol, who will join Newcastle United next year.
Australia are taking on Tunisia, Denmark and defending champions France in Group D and will open their World Cup campaign against Les Bleus on November 22.
AUSTRALIA 2022 WORLD CUP SQUAD IN FULL:
Goalkeepers: Mathew Ryan, Andrew Redmayne, Danny Vukovic
Defenders: Milos Degenek, Aziz Behich, Joel King, Nathaniel Atkinson, Fran Karacic, Harry Souttar, Kye Rowles, Bailey Wright, Thomas Deng
Midfielders: Aaron Mooy, Jackson Irvine, Ajdin Hrustic, Keanu Baccus, Cameron Devlin, Riley McGree
Forwards: Awer Mabil, Mathew Leckie, Martin Boyle, Jamie Maclaren, Jason Cummings, Mitchell Duke, Garang Kuol, Craig Goodwin