The former world number one was tearful after struggling through her last-16 match against defending champion Suzan Lamens in Osaka on Wednesday.
Top seed Osaka, who turned 28 this week, was supposed to face Romania's Jaqueline Cristian in the last eight.
"We regret to announce that Naomi Osaka has not recovered from a left leg injury sustained during the second round of this tournament and has withdrawn from the quarter-finals scheduled for today," the tournament said on X.
Osaka finished her three-set defeat of Lamens with heavy strapping on her left thigh and said afterward that only painkillers had helped her get through the match.
Her exit leaves fourth seed Leylah Fernandez as the highest-seeded player remaining in the draw.
Osaka, who is ranked 16th in the world, is supposed to play in the Pan Pacific Open in Tokyo next week.
