The four-time grand slam winner pulled out of Roland Garros on Monday, a day after tournament organisers said her continued refusal to attend mandatory press conferences could result in her being thrown out of the event.
Osaka said in a statement posted to social media that she has had bouts of depression since winning the US Open in 2018 and never intended for her stance to become a distraction.
Monday's action in Paris had mostly been completed when the news broke, but Serena Williams shared her thoughts following an evening match.
Williams acknowledged feeling anxious dealing with the press at times early in her career, but said she believed the experience made her stronger.
Top of mind, however, was concern for Osaka.
"The only thing I feel is that I feel for Naomi. I feel like I wish I could give her a hug because I know what it's like," Williams said.
"We have different personalities, and people are different. Not everyone is the same. Everyone is different and everyone handles things differently.
"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. I think she's doing the best that she can."
Osaka's fellow players and others took to social media with encouraging messages for the 23-year-old.
Venus Williams wrote on Instagram: "So proud of you. Take care of yourself and see you back winning soon!"
Young American star Coco Gauff responded to Osaka's tweet by writing "stay strong ... I admire your vulnerability."
A pair of tennis legends also weighed in on Twitter.
"I am so sad about Naomi Osaka. I truly hope she will be ok," Martina Navratilova wrote.
"As athletes we are taught to take care of our body, and perhaps the mental and emotional aspect gets short shrift.
"This is about more than doing or not doing a press conference. Good luck Naomi - we are all pulling for you!"
Billie Jean King added: "It’s incredibly brave that Naomi Osaka has revealed her truth about her struggle with depression. Right now, the important thing is that we give her the space and time she needs. We wish her well."
Mardy Fish, the former ATP player who reached number seven in the world, wrote to Osaka: "Mental health is nothing to criticise. Nothing to joke about. Pls [sic] take your mental health seriously. Without my support system, I truly believe I would not be here today. Here for you."
That public show of support extended beyond tennis, as prominent NFL and NBA players praised Osaka for her courage.
"We are with you," said Seattle Seahawks quarterback Russell Wilson.
NBA star Stephen Curry wrote: "You shouldn't ever have to make a decison like this - but so damn impressive taking the high road when the powers that be don't protect their own. Major respect."