BMW is recalling 29,868 Minis in the UK including the Cooper S and John Cooper Works models built between March 2006 and January 2011 because of a fault with an electric water pump.
The recall is in response to an incident involving an engine-related fire caused by the fault.
Customers will receive a letter inviting them to have the water pump replaced for free at a Mini dealership. The work is expected to take about an hour to complete.
BMW said there was a "very low incidence" of the fault and the vehicles remain safe to drive.
235,000 Minis are to be recalled worldwide.