The 13-year-old skater qualified for second place for the final at Ariake Urban Park, with a best score of 57.40.
After falling in her first two points of the final, she made her final attempt with a score of 56.47 to finish behind Japanese pair Sakura Yosozumi, 19, and Kokona Hiraki, 12.
After his series, Brown told the BBC: “It was crazy. It’s crazy. It’s crazy to be here, and skating with all the girls was really fun.
“Everyone’s torn. It’s great to be here. I didn’t think about the scores. But I’m really happy with this score – very happy. “
Brown’s achievement is all the more remarkable for the fractured skull and broken bones she suffered in a horrific fall in training last year.
The teenager posted a video clip of the fall to her Instagram account, which has nearly a million subscribers, with the message: “I’m thrilled to come back even stronger and stronger. My heart wants to go so hard right now. “
Brown, who was born in Miyazaki, Japan to a Japanese mother and a British father, competed in the US Open in 2016 at the age of eight and for the first time chose to compete for the Great Britain in 2018.
She warmed up for the Games by winning gold at the prestigious X Games last month, even though none of her main Olympic challengers, Okamoto and Hiraki, were in attendance.
Hiraki was the first of the main contenders for qualifying amid the hottest day of the Games so far, reaching 32 degrees with 90% humidity.