Media reports said Queen Elizabeth II's second son hit the officer as he was driving his four-by-four through the palace gates.
The palace confirmed Friday there had been "a minor incident" involving the prince and said it was a matter for the police.
The Metropolitan Police say an officer had been hit by a vehicle on Constitution Hill, outside the palace, and sustained minor arm injuries.
The force says it is investigating the circumstances of the crash.
The 49-year-old prince is known for his passion for cars. In 2002 he was stopped for speeding in his Range Rover but not charged.
