But the British number one tennis player still hopes to be fit to compete in singles competition at next month's Australian Open, which falls in between the two team events.
Draper had been due to fly to Australia on Monday before partnering with Katie Boulter for Britain at the United Cup, an international mixed team tournament in Sydney starting on December 30.
"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," said Draper in a statement on Thursday.
"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 now plans to travel to Melbourne later this month as he bids to be fit for the first Grand Slam tournament of 2025, which starts on January 12.
The injury comes at the end of a breakthrough year for Draper, who finished the 2024 season with a career-high ranking of 15 after winning his first two ATP Tour titles and also reached the US Open semi-finals.
And it has led him to withdraw from the Davis Cup first-round tie in Japan, which comes straight after the end of the Australian Open.
"Together with (British captain) Leon (Smith), we have also made the difficult decision for me to sit out the upcoming Davis Cup match in Japan in order to give me the opportunity post-Australian Open to complete the rehab and strengthening of my hip," said Draper.
