China's Yan Wang successfully defended her title with 14.988 points followed by Japan's Sae Miyakawa with 14.812 points. Karmakar, who also won a bronze in the 2014 Commonwealth Games in Glasgow, finished with 14.725 points in third.
Karmakar will turn 22 on August 9 and is a native of Agartala.
The Sports Authority of India took to Twitter to congratulate Karmakar on her bronze.
Earlier in February, Karmakar excelled with a total of five gold medals for Tripura in the 35th National Games in Kerala.
At the 2014 Asian Games, Karmakar finished fourth in the vault final with a score of 14.200.
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Home/Sports/Others/Indian Gymnast Dipa Karmakar Wins Bronze At Asian Championships