Daimler, the brand’s owner, launched a global recall of around one million vehicles worldwide.
Models involved in the recall include certain A-Class, B-Class, C-Class, E-Class and CLA cars and GLA and GLC SUVs.
An issue with some starter components in cars made between 2015 and 2017 is thought to cause them to overheat.
There have been reports of 51 fires, with about 30 in the US.
No injuries or deaths have been reported and it is not known if any of the fires occurred in the UK.
Daimler said the starting current limiter could overload under "unique" conditions where a driver repeatedly tries to start their car when the engine has seized up.
A Mercedes spokesman told Car Dealer magazine: "There are potentially 75,000 cars in the UK which will be affected by the recall. This is a recall which is yet to be issued."
The magazine said owners will be contacted in March.