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This is for the first time since winning a gold medal at the New Delhi Commonwealth Games 2010, Deepika will be out of a multi-discipline showpiece event.
Deepika crumbled at the crunch as An San won 6-0, clinching the first three sets.
Atanu Das will next meet Takaharu Furukawa of Japan on Saturday for a place in the quarterfinals of the individual competition.
Debutant boxer Pooja Rani (75kg) won her easy opening bout without a fuss to enter the last-eight stage.
Following the early exit of Atanu Das, Pravin Jadhav and Tarundeep Rai also crashed out in the round-of-32 stage of the men's individual event in Tokyo 2020 in Tokyo on Wednesday.
World No. 1 Deepika failed to notch up a single perfect 10 from eight arrows while Olympic debutant Jadhav misfired a six in the crucial fourth set after drilling in three perfect 10s.
The debutant was preferred by the Indian think-tank ahead of her husband and more experienced Atanu Das based on form shown in Friday's qualification round.
The world No.1 finished with 663 points, while 20-year-old Korean prodigy An San (680) topped the qualification round with an Olympic record score of 680.
The quartet of Deepika Kumari, Atanu Das, Tarundeep Rai and Pravin Jadhav entered the mega event with renewed hopes of winning the country's first Olympic medal in the sport.
Deepika held her nerve in an intriguing play-off to down Lisa Unruh.