Chan first injured his chest in March while shooting his recent action comedy "Rob-B-Hood," when a stunt man wearing the wrong shoes kicked him.
Chan said he got hit in the same area by a steel-reinforced wooden table while shooting a fight scene for "Rush Hour 3."
"I was in a lot of pain because it was in the same spot where I had gotten hurt during the filming of 'Rob-B-Hood,"' he said.
Chan said he tried to work through the pain, wearing a stunt belt across his upper chest and taking medication, but the movie's producers eventually sent him to a doctor. An X-ray cleared him of broken bones or organ injury, Chan said.
Chan has suffered numerous injuries throughout his career. One of his worst was a brain hemorrhage while filming "Armor of God." He said in an interview last year he usually feels pain in his waist, knees and shoulders when he wakes up.
The action star also said he's impressed with the spoken English of rising Chinese actress Zhang Jingchu, who has a part in "Rush Hour 3."
Chan said Zhang, whose credits include "Seven Swords" and "Peacock," has shown good acting skills, but that he was "also surprised that her English was so good."
"I don't know when she learned the language, but she sounded like an American. I've worked with many actresses who have had to learn English for a film, but she sounded the best," he said.
Zhang has said she has been studying English in her blog, reports AP.
The Chinese actress is making her U.S. debut in "Rush Hour 3," following in the footsteps of compatriot Zhang Ziyi, who made her debut in "Rush Hour 2" and has since successfully crossed over to Hollywood. The two Zhangs, who aren't related, have drawn comparisons to each other.
In "Rush Hour 3," Zhang Jingchu plays Soo Yung, the daughter of Chinese ambassador Han who is kidnapped in the first installment of the "Rush Hour" series, which also stars Chris Tucker.
The "Rush Hour" series plays on the humor from an interracial pairing of an ethnic Chinese and black police officer, played by Chan and Tucker.