Rapper Saweetie wrote, "Yes", alongside several flame emojis, while Venus Williams and Storm Reid chimed in with similar messages.
Another fan wrote, "Hope you are doing well and staying safe. Miss you so much thinking about you every day."
And one commented, "Hope you are well too!! Great Work, Thank you for vouching for us introverts."
"Gorgeous! So proud of you for taking care of yourself!" another person added.
The fashion shoot comes just a month after Osaka made headlines for withdrawing from the 2021 French Open amid backlash over her refusal to attend the tournament's press conferences. She explained that it was to protect her emotional and mental health, but was fined $15,000 as a result.
Osaka first made the announcement on social media, opening up about her struggles with 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 wrote.
"Anyone that knows me knows I'm introverted, and anyone that sees me at the tournaments will notice that I am often wearing headphones as that dulls my anxiety.
"Though the tennis press has always been kind to me (and I wanna apologize especially to all the cool journalists who I may have hurt), I am not a natural public speaker and get huge waves of anxiety before I speak to the world's media. I get really nervous and find it stressful to always try to engage and give you the best answers I can."
She also withdrew from Wimbledon last week. Since both exits, fans, celebrities and fellow athletes have flocked to her side to support her.
Japanese-American Osaka, who was born in Japan, plans to head to the Tokyo Olympics beginning on July 23. In a recent statement she said she's "excited to play in front of her home fans".
