In the last of the semi-finals, the Olympic silver medallist beat the week's giant killer 21-13, 21-10.
Chen, the world junior champion, had ousted the top seed, Akane Yumaguchi, and the 2013 champion, Ratchanok Intanon, on her way to the last four. But now she will have to settle for the bronze medal.
Sindhu will be hoping to one better than her compatriot, Saina Nehwal, who won the silver medal in 2015.
"I am very proud to make the final," said a delighted Sindhu after the unexpectedly one-sided semi. "I played very well today and now look forward to trying to win gold tomorrow."
Okuhara staged a great fightback from one game down to make it to the final day. She defeated Nehwal, 12-21, 21-17, 21-10, getting stronger as the match went on.
On Friday, the seventh seed had knocked out the reigning world and Olympic champion, Carolina Marin.
"I am so proud to have made it to the final, but now I want gold," she said. It is the first time a Japanese player has made it to the final of a world singles event.