Wood will return home later this week to work on his rehabilitation and recovery, the team said on Tuesday.
The 35-year-old's absence is a blow to an inexperienced England attack, who were well handled by Australia's batters at the Gabba, where the hosts won by eight wickets.
Perth was Wood's first Test in 15 months following a long period to rehabilitate the knee.
He said he was "gutted" in a post on social media but would do all he could to return to the international arena.
"After extensive surgery and seven long, hard months of work and rehab to get back into the Test arena, my knee just hasn't held up," he wrote.
"None of us expected this. I came here with high expectations about making a big impact.
"I'm desperately disappointed that despite yet more injections and intensive medical treatment, it has become clear that the flare-up in my knee is worse than feared."
Wood was ruled out on the same day Australia confirmed stalwart quick Josh Hazlewood would play no part in the Ashes following Achilles and hamstring injuries.
Surrey seamer Matthew Fisher has been added to the squad and will link up with the group this week, having been in Australia with the England Lions.
Fisher played his one Test during the 2022 tour of the West Indies.
England had Jofra Archer, Brydon Carse and Gus Atkinson in their pace attack at the Gabba, with all-rounder Ben Stokes offering a fourth seam option and Will Jacks providing part-time spin.
Australia posted 511 in their reply to England's first innings 334, with the tourists' bowlers frustrated for the better part of two sessions by the hosts' tail-enders.
Australia lead the five-Test series 2-0 and need only to draw the third match in Adelaide starting December 17th to retain the urn.