The 34-year-old prince was at a red light in Djurgården, near central Stockholm, when the incident occurred.
"I have spoken with the prince. He was back-ended by a bus at Berwaldhallen. He feels fine, but the back of the car was damaged," Annika Sönnerberg of the Royal Court told the Aftonbladet newspaper.
The prince then boarded the bus to confront the driver, much to the surprise of other passengers.
"He didn't want to make a scene when he saw that he had an audience," one witness told the Expressen newspaper, adding that the prince looked shocked.
It remains unclear whether the prince or the bus driver was at fault.
Prince Carl Philip, Duke of Värmland, is third in line to the throne after his older sister Victoria and her daughter Estelle.