The dumpster moving apparatus is a device capable of providing motorized assistance for moving large containers such as refuse dumpsters. The apparatus includes an enclosure containing a motor and having a pair of wheel assemblies. The electric motor is operatively coupled to the wheel assemblies to provide the motorized assistance for moving the container. The motor includes a transmission to provide for both forward and rearward variable-speed motion. A rechargeable battery pack and a control module supply electrical power and a control means to the motor. A tongue and hitch ball extend from a front portion of the enclosure to engage the container during a moving operation. In one (1) embodiment, the apparatus can include associated bracketry for removable connection of the device to a trash collection vehicle when not in use.