A drive apparatus which is compact in a height direction and a diametrical direction and with which a sufficient air breather function can be obtained, and a construction machine including the drive apparatus. The drive apparatus includes an electric motor and a speed reducer. An interior of a motor housing communicates with a speed reducer chamber such that a flow of air between the speed reducer chamber and the interior of the motor housing is permitted while limiting inflow of lubricating oil into the interior of the motor housing from the speed reducer chamber. An air breather passage and an air breather pipe for opening the interior of the motor housing to the atmosphere are provided in the motor housing.