An electric drive axle assembly and a vehicle having the same are provided. The electric drive axle assembly includes: an electric powertrain, an axle housing assembly, and a central parking module. The electric powertrain includes a power motor, a transmission and a differential with an input end and two output ends; and the power motor is connected to the input end of the differential through the transmission. The axle housing assembly includes an axle housing component and two half axles; the two half axles and the differential are disposed in the axle housing component; the two half axles are connected to the two output ends of the differential respectively; and the electric powertrain is installed on the axle housing component. The central parking module is installed on the axle housing component and used for braking the input end of the differential.