Kyrgios (27) has skipped the team event since 2019 but would have been a strong addition given his career-best form in recent weeks which included a run to a maiden Grand Slam final at Wimbledon.
"It would have been great to have Nick Kyrgios in the team but unfortunately he was unavailable for this tie," team captain Lleyton Hewitt said in a media release on Tuesday.
Australia is drawn in Pool C with Germany, France and Belgium for the September 13th-18th finals in Hamburg. Thanasi Kokkinakis, Alexei Popyrin, Jason Kubler and Wimbledon men's doubles champions Matt Ebden and Max Purcell were also included in Australia's six-man team.
Eliminated at the group stage last year, Australia are bidding for their 29th Davis Cup title and first since 2003.