A workpiece clamp apparatus includes: a robot arm having, at a distal-end portion thereof, a holding section for holding a workpiece; a hydraulic-fluid supply coupler provided at the distal-end portion of the robot arm; a hydraulic-fluid supply device for supplying a hydraulic fluid to the hydraulic-fluid supply coupler; a clamping device having a plurality of clamping members that grip the workpiece for machining with a machine tool; and a cylinder that has a hydraulic-fluid supply port to which the hydraulic-fluid supply coupler can be connected and that drives the clamping member in the workpiece-gripping direction as a result of the hydraulic fluid being supplied via the hydraulic-fluid supply port.