The worldwide recall applies to 2006–11 MINI Cooper S and John Cooper Works models following internal quality-control checks that spotted a fault with an additional water pump that is fitted in each vehicle.
BMW said in a statement that the water pump is drawing residual heat out of the turbocharger after the engine has been switched off, which prevents carbon build-up of the oil in the bearing.
Under high operating temperatures, an electro-migration can occur at the circuit board installed in the additional water pump.
The company added that the electro-migration is caused by plastic additives in conjunction with high temperatures and can lead to a failure of the additional water pump.
This, in turn, can lead to a failure of the additional water pump or smouldering, and the possibility of fire cannot be ruled out.
BMW maintains that there have been no accidents or injuries related to this issue, although four cases of fires have been confirmed globally, including one in the UK.
MINI customers are to be offered a free replacement water pump in a procedure that is said to take around an hour.