The parts are attached to vehicle exhausts and contain precious metals used to reduce the amount of dangerous gases that are pumped into the air.
Posting on social media, Edinburgh Police said: “We've recently received reports of catalytic converter thefts in Edinburgh.
“They can be attractive items to thieves due to the precious metals they contain (rhodium, platinum, palladium).
“Hybrid vehicles are frequently targeted as they have two power sources, therefore the converter is used less frequently and the metals less corroded.
“Vans and SUV’s are particularly at risk, as their high clearance makes access to the exhaust system easier”.
They added: “If you see anyone acting suspiciously near to your property or vehicles please contact the police immediately with as detailed a description as possible of any person(s) or vehicle(s) involved.
“Please call ‘999’ if an emergency and urgent police assistance is required or 101 to report the matter to the police.”
To reduce the risk of theft, police advise drivers to park in a locked garage where possible – or alternatively choose a well-lit, populated area ideally with CCTV.
Motorists are also told to avoid parking half on the pavement and half on the road, as this will make it easier for thieves to access the converter.
In car parks, they says you shoild park alongside other vehicles and face the bonnet towards a wall if possible, to make accessing the cat convertor more difficult.
RAC spokesman Simon Williams says: “Drivers are often oblivious of their vehicle’s catalytic converter being stolen. Our patrols are often called to attend cars that have suddenly become excessively noisy.
"On investigation it’s very often the case that the car’s catalytic converter has been stolen.
“We’d strongly recommend motorists get in the habit of taking extra precautions to guard against this type of crime. Generally-speaking, most car crime takes place at night, so it makes sense to park a vehicle in a well-lit and residential location, or ideally in a garage if available.
"When away from home, look for car parks that have security patrols and are covered by CCTV.”