The authority says it will seek funding to carry out a trial, which, if successful, could see the technology rolled out more widely.
The cameras would use noise sensors and number plate recognition to identify vehicles emitting noise over a specified level, with fines then issued to the offending drivers.
The idea was put forward at a meeting of the full council by Liberal Democrat councillor Nat Green, who said residents’ health was being impacted by noisy cars and motorcycles in his Shrewsbury town centre ward of Quarry and Coton Hill.
He said: “This motion sprung out of casework that came from the centre of town. It became abundantly clear that many residents were becoming increasingly exasperated with certain vehicles through the centre of town.
“With a little bit of investigation it became apparent that these matters could be addressed through the use of acoustic cameras.”
Councillor Green cited “very successful” trials carried out in several locations around the country by the Department for Transport (DfT) in 2019, and more recently in London by the Royal Borough of Kensington and Chelsea.
He said: “It may be that the type of vehicles in Kensington and Chelsea are slightly more exotic than the ones you’ll find in Shrewsbury, but nonetheless there is an issue with certain vehicles either deliberately or unintentionally being far too loud.
“Let’s be absolutely clear, this is really a form of tackling anti-social behaviour through the use of vehicles.
“It’s not intended to pick up, for example, emergency vehicles or HGVs going about their lawful business.
“I’m strongly of the opinion that this is a way to reduce a form of pollution which, far too often, we just put up with. In fact noise pollution is really detrimental to health, not just mental health but also physical health.
“I think if we can improve that in the centre of towns, and also in other areas, then I think we should be acting as the next council to take this forward.
“If Kensington and Chelsea can do it then why not Shropshire?”
Councillor Dean Carroll, portfolio holder for highways, said it was an “excellent” idea, adding that seeking external funding for a trial would “accelerate” the project as no money had been set aside in next year’s budget.
Fellow Shrewsbury councillors Rosemary Dartnall and Rob Wilson also backed the proposal, saying motorists doing noisy laps of the town was a well-known problem.
Councillor Viv Parry said she had also received “a lot of complaints” about noisy cars and motorcycles in Ludlow.
She said: “I feel that we have put up with it long enough. Over the years it has got worse and worse.
“People are racing each other around town in the day as well as the night.”
Councillor Dan Morris, who represents Burnell, added: “This does happen in the rural areas as well. Noise pollution is a particularly high threshold to prove, so any way of helping to do this is to be welcomed.”
The motion was unanimously supported.