Postecoglou recalled forward Tim Cahill, defender Matthew Spiranovic and goalkeeper Eugene Galekovic after they missed recent friendlies against Germany and Macedonia.
Aaron Mooy, Adam Federici and Luke Devere have dropped out.
"We've selected a relatively settled squad made up of the core of players that brought success at the Asian Cup but also the core of players that will take us through to the next World Cup," Postecoglou said in a statement released on Monday.
"This is the start of the next chapter in our journey and we are all excited about what lies ahead over the next two years.
"We've been open in our desire to make an impact at the 2018 World Cup but first we need to qualify and that task is immediately in front of us."
Postecoglou said the nucleus of his 2018 World Cup squad was already together and the team that went through qualifying would be very settled before the next global showpiece in Russia.
"We'll work on building a strong base and then over the next two years we can expose more players to the squad as form and fitness warrants selection but those players will come into a settled unit when they get an opportunity," he added.
The team will hold a week-long training camp in Dubai before travelling to Bishkek for the June 16 clash.
Squad:
Goalkeepers - Mathew Ryan (Club Bruges), Mitchell Langerak
(Borussia Dortmund), Eugene Galekovic (Adelaide United)
Defenders - Matthew Spiranovic (Western Sydney Wanderers), Trent Sainsbury (PEC Zwolle), Alex Wilkinson (Jeonbuk Hyundai Motors), Izaz Behich (Bursaspor), Jason Davidson (West Bromwich Albion), Ivan Franjic (unattached), Tarek Elrich (Adelaide United), Bailey Wright (Preston North End)
Midfielders - Mark Milligan (Melbourne Victory), Mile Jedinak (Crystal Palace), Tommy Oar (Utrecht), Massimo Luongo (Swindon), James Troisi (Zulte Waregem), Matt McKay (Brisbane Roar), Chris Ikonomidis (Lazio), Oliver Bozanic (FC Luzern)
Forwards - Tim Cahill (Shanghai Shenhua), Matthew Leckie (FC Ingolstadt), Tomi Juric (Western Sydney Wanderers), Nathan Burns (Wellington Phoenix)
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)
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