Disclosed are a vehicle engine control apparatus and a vehicle engine control method. An engine of a vehicle is turned off after a predetermined time elapses when a user gets off the vehicle with a smart key after stopping the vehicle indoors (e.g., a garage or an underground parking lot) while the engine is in an ON state. The engine of the vehicle is maintained in the ON state when there is a user's request. Thus, the ON/OFF state of the engine of the vehicle is may be controlled depending on the user's situation.