Audi reports a fault in an earth connection to the system could occur due to excessive thermo-mechanical strain on the unit's components.
If the condition occurs, this can limit the ability of both the ABS and ESC systems to stabilise the vehicle in an emergency situation, such as oversteer, understeer or hard braking.
Owners of the recalled units will be contacted directly by Audi Australia, and are advised to contact their local dealer to arrange the inspection and repair of their vehicle.
Audi says until the new software has been installed to their ESC control unit, owners should keep their A3 "well within" its handling limits by adjusting their speed "in advance to suit the visibility, weather, road and traffic conditions".
For more information, contacted 1800 502 834 (1800 50 AUDI).