Osaka said in the build-up to the tournament that she would not attend the obligatory press conferences for players after matches, saying the questioning by journalists stresses her mental health.
The four-time grand slam champion made good on her threat on Sunday when, after winning her first round match, she did not hold a press conference.
She was fined $15,000 ($A19,400) by the Roland Garros referee, and grand slam organisers later issued a strongly worded statement warning of possible expulsion from the French Open and future majors if she failed to change her stance.
On Monday, the 23-year-old Osaka took matters into her own hands to end the stand-off.
"This isn't a situation I ever imagined or intended when I posted a few days ago," the world No.2 posted on Twitter.
"I think now the best thing for the tournament, the other players and my well-being is that I withdraw so that everyone can get back to focusing on the tennis going on in Paris.
"I never wanted to be a distraction and I accept that my timing was not ideal and my message could have been clearer."
Osaka, one of the biggest names in women's sport, went on to say she had suffered from depression.
"The truth is that I have suffered long bouts of depression since the US Open in 2018 and I have had a really hard time coping with that," she said.
"Anyone that knows me knows I'm introverted, and anyone that has seen me at the tournaments will notice that I'm often wearing headphones as that helps dull my social anxiety."
The French Tennis Federation, organisers of the tournament, called her withdrawal "unfortunate" while the Women's Tennis Association said mental health was one of the highest priorities of the organisation.
After beating Serena Williams at Flushing Meadows to claim her first major in 2018, Osaka was booed by the crowd during the presentation ceremony as her victory was overshadowed by the American's outburst after a row with the umpire.
Osaka said that since then she has struggled in the spotlight, suffering "huge waves of anxiety" before speaking to the world's media.
Williams, after her first-round match in Paris, offered her support to Osaka.
"You just have to let her handle it the way she wants to, in the best way she thinks she can, and that's the only thing I can say," Williams said.
"I think she's doing the best that she can."
Osaka tweeted that she would take some time away from tennis and hoped later to meet the sport's organisers to improve the system for "the players, press and fans".
Wimbledon starts in four weeks, while Osaka's next tournament is scheduled to be in Berlin on grass in two weeks' time.