The former British number one was set to play the United States' Robin Montgomery at the event on Tuesday (31.12.24), but she has had to withdraw due to picking up a "back niggle".
The 22-year-old U.S. Open champion will now fly to Melbourne to prepare for the Australian Open, which kicks off on January 12.
She told the WTA: "I’ve tried my best to be ready.
"I love Auckland and the fans here. But, unfortunately, I’ve picked up a back niggle, and I won’t be ready in time."
Last season saw Emma miss out on March's Miami Open with a back problem, as well as only taking part in 10 matches following her Wimbledon appearance.
She also withdrew from several Asian tournaments after sustaining a foot injury during a Korea Open quarter-final match in September.
Emma – who has been in Auckland with fitness trainer Yutaka Nakamura – is set to take part in the first Grand Slam of the season next year without any practice.
The Toronto-born star previously admitted she prioritises her health over results.
She said in an interview with HSBC: "I'm just more grateful for my health than results."