Sindhu frittered away a one-game lead to lose 21-16 16-21 19-21 in a thrilling quarterfinal match that lasted one hour and six minutes.
World number six Sindhu had a 4-2 head-to-head record against the 14th ranked Japanese before Thursday's match.
Takahashi had defeated another top Indian, Saina Nehwal, in the second round.
With the defeat of Sindhu, India's campaign in the BWF Super 500 tournament came to an end.
World championships bronze medallist B Sai Praneeth, Kidambi Srikanth and Sourabh Verma crashed out of the tournament in the second round on Wednesday.
Indians thus continued their poor form after making early exits in the Malaysia Masters last week. Sindhu and Saina had reached the quarterfinals in Kuala Lumpur but none of the men's singles players could cross the second round.
Sindhu began well, breaking away 11-6 in the first game. The Japanese later caught up with the Indian and took the score line to 11-12. But Sindhu was in no mood to allow her opponent to claw her way back and she was 16-15 up. She took the remaining five points with ease to take the first game.
One game up in the match, Sindhu, however, seemed to have let her guard off a bit as she trailed all through the second game which she lost 16-21.
Takahashi straightaway took a 7-0 lead but Sindhu fought back to reduce the gap to 4-8. The Indian could not sustain the tempo as she trailed 6-15. She recovered midway but found herself trailing 15-20 before losing the second game.
The decider was a close contest with Takahashi 3-0 up only to see Sindhu making it 3-3. Both the players fought a see-saw battle as they were locked 10-10 and then 15-15. But from 18-18, Takahashi broke away to be at 20-18. Sindhu saved one match point but the Japanese took the next to make the semifinals.