Osaka had hit the headlines by revealing she would not face the media at Roland Garros because "people have no regard for athletes' mental health" during news conferences.
The four-time grand slam champion was fined for not fulfilling her media duties after beating Maria Tig and warned she could face more severe sanctions.
Osaka on Monday revealed she had pulled out of the second major of the year to take time away from the court, having struggled with "long bouts of depression" since winning the US Open in 2018.
The 23-year-old also spoke of her struggles with social anxiety and Becker is concerned for her tennis future.
Becker, a winner of six grand slam titles in his illustrious career, told Eurosport: "I heard her first response a couple of days ago about this media boycott and that is something to be always taken seriously, especially from such a young woman.
"She couldn't cope with the pressures of facing the media after she loses a match, but that happens frequently and you have to deal with it.
"I always believed the media was part of the job. Without the media, there is no prize money, no contracts, you don't get half the cake. I hated the media and I didn't like talking to journalists, but you had to do it.
"Now she is pulling out of the tournament altogether because she can't cope with it and that raises much bigger questions for me.
"If she can't cope with the media in Paris, she can't cope with the media in Wimbledon or the US Open. So I almost feel like her career is in danger due to mental health issues."