She participated in the 2016 Japan Women's Open Golf Championship where she made the cut and finished tied for 28th place.

Furue won the 2019 Fujitsu Ladies on the LPGA of Japan Tour as an amateur, thus was awarded exemption of the JLPGA Player Certification Test, and turned professional shortly afterwards.

She was in contention at the 2021 Evian Championship where she birdied three of the last four holes to claim fourth ahead of Atthaya Thitikul.

[5] At the 2021 Women's British Open, Furue started the final round four shots behind co-leaders Anna Nordqvist and Nanna Koerstz Madsen, but lost ground on the leaders and ended tied for 20th as she carded a level-par round of 72 that featured an eagle, two birdies and four bogeys.

[7] She won her first LPGA Tour tournament, at the Trust Golf Women's Scottish Open on 31 July 2022, shooting a course record 10-under-par 62 (267, −21) in the final round to win by three strokes over Céline Boutier, after trailing by four strokes after 54 holes to co-leaders Boutier and Lydia Ko.