The Olympic swimmer had been travelling in a Cadillac Escalade with two passengers when the incident occurred at an intersection at around 9pm. All three were unhurt.
The female driver of the second car was reportedly left "shaken up" by the collision and was taken to hospital as a precaution.
Police spokesman Anthony Gulielmi told reporters at the scene that Phelps had been interviewed by police but that alcohol was not thought to be involved. No charges were issued and the accident remains under investigation.
Phelps gained worldwide fame when he won eight gold medals at the Beijing Olympics. He recently picked up a further five golds and one silver medal at the World Swimming Championships.