The four-time grand slam champion announced on social media before the tournament that she would not be doing any press at Roland Garros, citing mental health reasons.
It has not gone down well with the tournament and drew an unusually punchy joint statement from the board of the four grand slams, who threatened Osaka with severe sanctions should she not reconsider her stance.
"We have advised Naomi Osaka that, should she continue to ignore her media obligations during the tournament, she would be exposing herself to possible further code of conduct infringement consequences," the statement read.
"As might be expected, repeat violations attract tougher sanctions including default from the tournament and the trigger of a major offence investigation that could lead to more substantial fines and future grand slam suspensions."
Osaka has been fined $US15,000 ($A19,500) for refusing to fulfil her media commitments after a 6-4 7-6 (7-4) first-round victory over Patricia Maria Tig.
"The Roland Garros teams asked her to reconsider her position and tried unsuccessfully to speak with her to check on her well-being, understand the specifics of her issue and what might be done to address it on site..." the joint statement continued.
"As a sport, there is nothing more important than ensuring no player has an unfair advantage over another, which unfortunately is the case in this situation if one player refuses to dedicate time to participate in media commitments while the others all honour their commitments.
"Finally, all grand slams remain committed to continually reviewing and discussing opportunities, together with the tours and the players, to improve every aspect of the player experience, including with the media.
"But we consider this is only ever achieved through respectful and constructive discussions."
In an apparent riposte on Twitter on Sunday evening, the Japanese star wrote: "anger is a lack of understanding. change makes people uncomfortable."
Despite her media snub, Osaka did take part in a short and rather awkward on-court interview for the few hundred fans allowed into Court Philippe Chatrier after her victory over Romanian Tig.
"I'm very glad that I won," said the 23-year-old Osaka, who skipped the tournament last year after winning her third slam title at the US Open.
"It's a very beautiful court. I've only played two matches here, one was before the roof and one is right now. Hopefully I'll keep it going."
Osaka, who lives in Florida, has never made it past the third round at Roland Garros and arrived in Paris having played only three matches on clay this season after early defeats in Madrid and Rome.
Analysis and discussion with Pat Rafter tonight on The Project, 6.30pm on 10 and 10 Play.