It was the second major surprise in a week involving U.S. Open champion Osaka, who announced she had parted ways with Sascha Bajin, the coach who had guided her in both her Grand Slam victories.
"This match is the result of that," Osaka told reporters of her coaching shake-up. "I'm pretty sure as time goes on you guys will stop talking about it. For now, it's like the biggest tennis news, I guess.
"See, it's a little bit hard because I feel like people are staring at me, and not in a good way."
The hard-hitting Osaka has become one of tennis's most bankable players since upsetting American great Serena Williams in the final at Flushing Meadows but has always spoken of feeling uncomfortable in the spotlight.
Osaka wiped away tears as she spoke of the challenge of adjusting to her new celebrity.
"I don't think I necessarily understand what position I'm in in a way," she said.
"And because last year I wasn't even anywhere close to this ranking and people didn't pay attention to me and that's something that I'm comfortable with.
"I don't know why I'm crying," she said with a smile. "I don't know why this is happening. I don't really like the attention, so yeah, it's been a little tough."
Mladenovic, ranked 67th, hit less winners than Osaka but converted seven of 10 break points to claim her first win over a world number one.
"It means a lot, honestly," Mladenovic said after booking a match with a Spain's Carla Suarez Navarro in the last 16.
"I know I'm capable of beating great players."
Osaka aside, most of the other big names progressed safely to the third round.
Australian Open runner-up Petra Kvitova rallied from a set down to beat Czech compatriot Katerina Siniakova 6-7(3) 6-4 6-4, while third seed Simona Halep advanced with a 7-6(4) 6-4 victory over Canadian wildcard Eugenie Bouchard.
Kvitova, the second seed, was almost the architect of her downfall with nine double-faults in the match, but recovered to set up a match with American qualifier Jennifer Brady.
Brady pulled off another of the day's upsets when she beat 14th seed Caroline Garcia 6-4 7-5, joining compatriot Sofia Kenin in the next round.
Defending champion Elina Svitolina also advanced after her second round opponent Ons Jabeur of Tunisia was forced to retire with an apparent shoulder injury while trailing 7-6(4) 4-0.
(Reporting by Simon Jennings in Bengaluru and Ian Ransom in Melbourne; Editing by Hugh Lawson and Christian Radnedge and Greg Stutchbury)
