There were also reports of a large limestone rock thrown through the windscreen of a vehicle travelling on Old Coast Road, Dawesville at 11.45am on Saturday.
The elderly female driver was said to be distressed.
Senior-Sergeant Dean Snashall said there had been a spate of rocks thrown at vehicles in the past month.
A Mandurah Taxis spokeswoman warned someone could be killed by the missiles.
She reported rocks, bottles and lumps of concrete had been thrown at taxis. She said the company forked out about $1000 each week for repairs to vehicles from missiles thrown at them, people kicking cars, mirrors ripped off and graffiti.
Sgt Snashall said 27-year-old Matthew Vroom had been delivering newspapers in a work vehicle about 1am on April 14. The vehicle was on Mandurah Road, just north of Pinjarra Road, when a rock was thrown through an open window.
Sgt Snashall said there was blood everywhere. Mr Vroom was able to drive to Peel Health Campus, where staff used surgical glue to treat a cut on his jaw.
The rock-throwing incidents occur mainly at weekends, in the early hours of the morning.
‘Until now, there had only been reports of damage and dents to cars,’ Sgt Snashall said.
The Mandurah Taxis spokeswoman said missiles thrown at vehicles was a real issue and it was happening every weekend.
Trouble spots included Old Coast Road, Halls Head, Erskine, Falcon, Coodanup and Greenfields.
‘Our buses (that have been modified to cater for disabled people) get damaged on the weekends and it inconveniences those with disabilities when the bus needs to get repaired through the week,’ the spokeswoman said.
She wants external recording equipment to be fitted to taxis, similar to taxis in Perth. She said such technology could help in identifying offenders.