No one was injured.
The incident occurred at the couple's estate on the island of Anglesey, Wales.
"Shortly before 1 p.m. Wednesday ... an on-duty MPS [Metropolitan Police Service] police officer unintentionally discharged a firearm while in an unmarked police vehicle. The round damaged the floor of the vehicle. Another on-duty officer was in the vehicle at the time of the incident," a police spokesman said.
The unnamed officer whose gun discharged was suspended from duty until an investigation is completed, The Daily Telegraph reported Friday.
It was not clear if William and Kate were home when the shot was fired, CNN said.
William is a helicopter pilot in the Royal Air Force and stationed nearby.