Naomi lost to Czech Marketa Vondrosova, in two sets, to no avail, to be bid farewell early.
The first set ended 1-6 before Vondrosova won 6-4 in the second set.
The second-ranked Osaka was the favorite to win a medal at the Tokyo Olympics.
The surprise exit for Osaka comes because of its loss to the 42nd ranked world.
The Egyptian Mayar Sherif participated in the Tokyo Olympics and was qualified in the 64th round.
Mayar Sherif played the Tokyo Olympics in a historic achievement as the first Egyptian to participate in the Olympics in tennis.