The patient had endured years of severe pain and debilitating health complications due to the tumour
Japanese media said the duo, known as "A Masso," made the remark during a Sunday event, the same day that Osaka lifted her first trophy since winning the Australian Open in January, and also said that "she is too sunburned."
In separate messages carried on the website of their management company, Watanabe Entertainment Co Ltd, both women apologised for making "inappropriate, hurtful remarks" but did not refer to Osaka, who is Haitian and Japanese, by name.
"Though we should have thought about it, we made remarks that hurt many people, something we will never do again," Ai Murakami wrote.
"We sincerely apologise for making the specific person feel uncomfortable, as well as for everyone else connected to the event. We also sincerely apologise for causing trouble."
Watanabe Entertainment, also without naming Osaka, added their own apology for "remarks inconsiderate of diversity in an era where diversity is respected," saying the duo had been severely warned and steps taken to raise their awareness of the issue.
Neither Watanabe Entertainment nor Naomi Osaka's management office in Japan was immediately available to comment.
Osaka, who will turn 22 next month, was born in Japan to a Haitian father and Japanese mother but moved to the United States when she was young.
She has been widely hailed in Japan, which has traditionally seen itself as a racially homogeneous country, although successful mixed-race athletes such as Osaka herself, sprinter Asuka Cambridge and baseball pitcher Yu Darvish are challenging that image.
In January, Japanese noodle company Nissin had to remove a controversial commercial in which a cartoon character depicting Osaka was shown with pale skin and light brown hair after it prompted an outcry. Nissin said it had not intended to "whitewash" Osaka and promised to pay more attention to diversity issues.
The patient had endured years of severe pain and debilitating health complications due to the tumour
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