Media playback is not supported on this device
The 26-year-old's left arm was bitten off in a shark attack in 2003.
The Hawaiian beat six-time world champion Stephanie Gilmore and world number one Tyler Wright before losing to the winner, France's Johanne Defay, in the semi-finals.
She tweeted: "Beyond stoked to finish 3rd... as the wildcard! LOVED competing & looking forward to more adventures."
It is the sixth time Hamilton, who had a child last year, has competed on the elite level World Surf League tour, with her trip to the semi-finals seeing her surpass her previous best finish of ninth in 2010.
Hamilton was 13 when a huge tiger shark mauled her, causing her to lose 60% of her blood after it ripped off her arm.
But she was back on a board less than a month after the near-fatal attack, with her story later inspiring the 2011 Hollywood film "Soul Surfer" featuring Dennis Quaid and Helen Hunt.
Hamilton embarked on intensive physical therapy and strengthening exercises to adjust her balance and movements to compensate for the missing arm.
The only concession made to her handicap is a handle on the surfboard, which allows her to duck-dive under approaching waves when she paddles out.
"I know I'm in a unique position to hopefully encourage young girls to chase their dreams," she added.
"Even after losing my arm I'm still doing everything I hoped I could do. I'm a reminder for young girls that you can do it if you set your mind to it."
One-armed surfer Bethany Hamilton finished a career-best third in the World Surf League's Fiji Women's Pro.