Draper sustained the problem during pre-season training and was forced to miss a scheduled practice week with Carlos Alcaraz in Spain.
He had been due to fly out to Australia on Monday before playing with Katie Boulter for Britain at the United Cup team event in Sydney beginning on December 30.
He cannot be replaced in the United Cup team so Billy Harris, ranked No.125, will step up.
Draper said: "As I work to get on top of my hip injury and get match-fit, I have unfortunately been advised not to play in the United Cup.
"While we are very positive about competing in the Australian Open this year, I know I won't be able to jump straight into a packed schedule as I manage and strengthen my hip. (I'm) gutted as I was really looking forward to playing in the United Cup for the first time."
The 22-year-old is now planning to fly to Melbourne later this month as he races to be fit for the opening grand slam of the new season, which starts on January 12.
The news is a setback for Draper, who finished the 2024 season at a career-high ranking of 15 after winning his first two ATP Tour titles, reaching the semi-finals of the US Open and, crucially, avoiding the injury issues that had dogged him in the past.
He has also decided to miss the Davis Cup first-round tie in Japan, which immediately follows the Australian Open.
Draper's absence could mean a debut for Scot Jacob Fearnley, who has soared up the rankings to 99 this season, making him British number three behind Draper and Cameron Norrie.
- with AAP
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