The Scot is set to undergo further medical treatment for an ongoing gallstones problem.
The 52-year-old revealed his health issue before last week's World Matchplay, and said he was "trying not to eat crumpets caked in butter" in a bid to participate in Blackpool.
Snakebite did play in the Matchplay and reached the quarter-final with victories over Madars Razma and Krzysztof Ratajski.
Ultimately, the current world champion was knocked out by Belgium's Dimitri Van den Bergh who, coincidentally, is the man who will replace Wright at the World Series of Darts.
Wright told the Professional Darts Corporation's official website: "I'm devastated to have to miss the visits to Australia and New Zealand but after further medical checks I have to put my health first.
"I was really looking forward to finally getting to Australia and New Zealand and being introduced Down Under as the reigning world champion in front of all the great fans there.
"I'll be doing everything I can to retain the World Championship and be back there next year instead!"