Babita lost to Zhuldyz Eshimova-Turtbayeva of Kazakhstan 3-6 in a hard-fought bronze medal play-off.
Earlier, Babita failed to enter the final of her weight division after losing her semifinal bout to Pak Yong-Mi of North Korea in another well-fought contest.
But in the initial two rounds, Babita had comfortably defeated Abdy Kadyrova Elsa Kyrgyzstan by TF, 10-0 in the quarterfinal, after getting the better of Zukhra Mustanova of Uzbekistan by the same margin in the qualification round.
In 63kg division, Aneeta outplayed Choi Jiae of Korea 6-1 in the qualification round but failed to overcome the challenge from China's Zhuo Ma Xiluo, losing 0-10 in her semifinal bout to miss out on a chance to fight for the gold medal.
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Aneeta got an opportunity to bag a bronze but she lost to her Mongolian rival Enkhbayar Tsevegmid in the third-fourth place bout and had to return empty handed in the end.
Sakshi Malik, meanwhile, won two of her four bouts that she fought today in 60kg category.
In the fifth round, however, the Indian girl beat Kazakhstan's Ayaulym Kassymova 8-1.
India's campaign got over early in 69kg weight category as Suman Kundu lost 0-6 by 'Fall' verdict to Kayoko Kudo of Japan in the quarterfinal.
Last night, Vinesh claimed the silver medal in women's 48kg division after losing her final bout to Japan's Yuki Irie, while Narsingh Pancham Yadav bagged a bronze in men's freestyle 74kg category.