Fleming and Flowers were in a van and taken to a hospital as a precaution and were released, Carney said. Neither Biden nor anyone else in his party was involved in the accident.
The two former Olympians later attended a figure skating competition, sitting in the row in front of Biden.
Olympic authorities said the accident happened shortly before noon. Fleming and Flowers were in the motorcade's next-to-last vehicle, which was rear-ended and hit the car in front of it.
Scott Gordon, spokesman for the Integrated Security Unit, said the accident was possibly caused by poor road conditions and perhaps an oil slick.
Fleming won the gold medal at the 1968 Grenoble Olympics. Flowers won gold at the 2002 Salt Lake City Games.
