The silver Ford Fiesta was hit as it passed under Naburn Bridge, between Selby and York, shattering the car's driver-side wing mirror.
It happened at around 8.25pm on Friday, May 30th. Investigating officers are appealing for anyone who witnessed the incident to come forward.
PC Peter Taylforth of York Police said, “Thankfully the woman driving the car was not injured as a result of this utterly reckless act of mindless stupidity. However she was naturally left very shaken by the experience.
“The person responsible demonstrated a complete disregard safety of the car’s occupants. Had the stone hit the windscreen the consequences could have been far more serious.
He added, “As Naburn Bridge is popular with walkers and cyclists I am sure someone may have noticed people acting in a suspicious manner, and urge them to get in touch straight away as they may have vital information which could help my enquiries.”
Or call Crimestoppers anonymously on 0800 555111, quoting reference number 12140087069.