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Deepika lost to the world No. 2 4-6 after sharing the first four sets.
Ankita and Deepika were the weakest links in the team as they failed to live up to expectations.
Ankita Bhakat bagged the 11th spot with a season-best score of 666, Deepika Kumari settled for 23rd place.
India, who have never won an Olympic archery medal, will send a full six-member contingent to Paris to compete in all five events for the first time in 12 years.
India will compete in all five medal events in archery in Paris -- men's and women's team, individual and mixed categories.
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.
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