Last month, Osaka withdrew from Roland Garros and announced she would "take some time away from the court" after she was fined $15,000 for skipping the news conference after her first-round victory.
The 23-year-old was also threatened by all four Grand Slam tournaments with the possibility of disqualification or suspension if she continued to avoid the media.
Osaka said she experienced anxiety before speaking to the media and revealed she suffered bouts of depression.
Speaking to BBC Sport, Murray said he hopes Osaka can return to the court when she feels better but added the situation could have been handled better.
"I really hope that she gets better and that she gets the help that she needs to feel better," he said.
"I believe that tennis will work with her and her team to find solutions to whatever it is that's triggering her anxiety or depression. I wish it'd been handled differently because I don't think anybody came out of it well.
"I can't believe her team, if press was what was making her feel depressed or anxious, hadn't communicated that to the Grand Slams or to the WTA to try to find a solution around it.
Osaka also pulled out of the Berlin WTA 5000 grass-court which began on Monday while French Open organisers defended their "pragmatic stance" in their dealings with four-time major champion.
"And I don't think it was a good look for the tours in terms of wanting to default her," Murray added.
"As soon as she said on social media that she'd been dealing with depression, the stance from the Slams and tennis changed and was quite different.
"But I do feel if I went to the Grand Slams [and said] that this is what I'm dealing with, and spoke to them directly, they would try to help."
Murray returns to action at Queens this week to take part in his first singles match since the Rotterdam Open in March.