Just 11 days before the start of the Australian Open, Emma was forced to retire from her second-round match due to an ankle injury.
The 20-year-old British woman won the first set but lost the second.
She withdrew two points into her first service game after receiving medical attention.
The match was played indoors because of the rain.
After an exhibition match in December, she said she was injury-free and feeling good, even though she had retired from five matches in the previous year.
She won her first match in New Zealand in preparation for the first major tournament in Australia.
In New Zealand, Coco Gauff beat the winner of the Australian Open to reach the quarter-finals.
The 18-year-old number one seed will next play China's Zhu Lin, who defeated seven-time Grand Slam singles champion Venus Williams in a rain-interrupted match that had to be moved on to an indoor court.
She came from behind in the deciding set to win the last four games. The Chinese world number 84 broke and saved four break points as she held serve to take a 5-5 lead before Williams broke again.
It was raining and windy outside. "It was tennis, but it was more about surviving than playing great," said Williams, who has been given a chance to play in the Australian Open.
It was different indoors but I have to hit a lot of balls.
The Czech Republic's Linda Noskova will play Victoria Azarenka in the quarter-finals. In other matches, Noskova beat the United States' Claire Liu, while Azarenka defeated China's Zheng Qinwen.
Tunisia's world number two Ons Jabeur advanced to the last eight with a 6-7 (7-3) 6-1 win over Sorana Cirstea.
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