West Mercia's police and crime commissioner criticised the attack, saying it could have stopped the police from attending an emergency.
Newport's Safer Neighbourhood Team's car was targeted by vandals while it was parked at the common in Donnington between 3.30pm and 4pm on Tuesday.
The tyres on the vehicle were slashed while the team was out dealing with an incident, and police have now said the tyres were let down with a "small, sharp object".
John-Paul Campion, Police and Crime Commissioner for West Merica Police, said the act could have stopped the police from attending a real emergency and helping people.
"Damaging a police car may be seen by some as an act challenging authority but police vehicles are used to get to those that need help in an emergency," he said.
"In reality of damaging a police car means may have stopped someone getting the help they need when they need it."
Newport police team tweeted: "Much as someone probably found it very amusing to let down the tyres on our vehicle whilst officers were attending an incident in Donnington, this now means it is off the road, unable to respond to incidents and potentially facing an unnecessary repair bill at taxpayers' expense.
"Once the tyre repair company had checked the tyres it was found the sidewalls of two of them had been punctured with a small, sharp object. Any info to 101 or @CrimestoppersUK."
The police are now looking for the culprit and said they may be carrying a knife so anyone with any information should contact 101 or Crimestoppers UK anonymously.
Damaging a police car may be seen by some as an act challenging authority but police vehicles are used to get to those that need help in an emergency. In reality of damaging a police car means may have stopped someone getting the help they need when they need it. https://t.co/YfqjL1LOum— John-Paul Campion (@JohnPaulCampion) June 9, 2021
Telford Cops tweeted: "Further checks show the tyres were slashed while it was parked on the common, Donnington between 3:30pm and 4pm. The suspect may be carrying a knife so we are keen for any help identifying them."