An electric drive unit for a motor vehicle comprises an electric motor having a motor housing, a stator mounted in the motor housing and having coil-wound poles, a rotor arranged internally of the stator with an air gap present between the stator and the rotor, and a planetary gear system having a sun wheel, a planet carrier, planet wheels and a ring gear. The planet wheels have a maximum diameter and axial positioning that an imaginary common envelope cylinder for all maximum diameters of the planet wheels is located radially inside of the winding heads present on one axial side of the stator and axially beside the portion of the rotor adjoining the air gap and that the planet wheels project in axial direction outwardly beyond said winding heads either not at all or with less than 50% of their tooth width in engagement with the sun wheel.