Tom Rogic and Mark Birighitti were also cut as Australia - who reduced their preliminary squad to 27 last week – continue their preparations for Brazil.
But it is the absence of Kennedy and Wilkshire that will grab the headlines, with the experienced pair both having represented Australia at the 2006 and 2010 tournaments.
"Every step of the selection process has been difficult because the players have worked very hard since they came into camp, but we have had to weigh up form, fitness and squad balance in coming up with the 23 players who will represent Australia at the 2014 World Cup," Postecoglou said to Football Federation Australia's official website.
"We've selected a squad that can do Australia proud and they will walk out onto the pitch for the World Cup in the green-and-gold shirt and display the characteristics that define our country."
Kennedy has played just eight games for Nagoya Grampus in this J.League season, scoring four goals, as he continues to manage a back issue which forced him of Australia's 2-0 friendly win over Parana Clube on Monday.
Last season's A-League top scorer, Newcastle Jets forward Adam Taggart, netted in that game to suggest that Kennedy's absence may not be too keenly felt, despite him scoring the goal that secured Australia's place at the World Cup.
Meanwhile, Dinamo Moscow man Wilkshire played 90 minutes in the friendly but clearly did not impress Postecoglou.
With Kennedy and Wilkshire both omitted, Australia have just five survivors from their ill-fated 2010 World Cup campaign. Heading the list of those five is Australia's all-time top scorer Tim Cahill and he is joined by Mark Bresciano, Mile Jedinak, Dario Vidosic and Mark Milligan.
Australia are heavily unfancied to progress from a difficult Group B that contains defending champions Spain and 2010 finalists Netherlands. Postecoglou's men begin their campaign with a crucial clash against Chile in Cuiaba on June 13.
Squad in full:
Goalkeepers: Eugene Galekovic (Adelaide United), Mitch Langerak (Borussia Dortmund), Mat Ryan (Club Brugge)
Defenders: Jason Davidson (Heracles), Ivan Franjic (Brisbane Roar), Ryan McGowan (Shandong Luneng), Matthew Spiranovic (Western Sydney Wanderers), Alex Wilkinson (Jeonbuk Motors), Bailey Wright (Preston North End).
Midfielders: Oliver Bozanic (Luzern), Mark Bresciano (Al Gharafa), James Holland (Austria Vienna), Mile Jedinak (Crystal Palace), Massimo Luongo (Swindon Town), Matt McKay (Brisbane Roar), Mark Milligan (Melbourne Victory), Dario Vidosic (Sion)
Forwards: Tim Cahill (New York Red Bulls), Ben Halloran (Fortuna Dusseldorf), Mathew Leckie (FSV Frankfurt), Tommy Oar (Utrecht), Adam Taggart (Newcastle Jets), James Troisi (Atalanta)