Soft wearable robots could provide support for lower and upper limbs, increase weight lifting ability, decrease energy required for walking and running, and even provide haptic feedback. However, to date most of wearable robots are based on electromagnetic motors or fluidic actuators, the former being rigid and bulky, the latter requiring external pumps or compressors, greatly limiting integration and portability. Here we describe a new class of electrically-driven soft fluidic muscles combining thin, fiber-like McKibben actuators with fully Stretchable Pumps. These pumps rely on ElectroHydroDynamics, a solid-state pumping mechanism that directly accelerates liquid molecules by means of an electric field. Requiring no moving parts, these pumps are silent and can be bent and stretched while operating. Each electrically-driven fluidic muscle consists of one Stretchable Pump and one thin McKibben actuator, resulting in a slender soft device weighing 2 g. We characterized the response of these devices, obtaining a blocked force of 0.84 N and a maximum stroke of 4 mm. Future work will focus on decreasing the response time and increasing the energy efficiency. Modular and straightforward to integrate in textiles, these electrically-driven fluidic muscles will enable soft smart clothing with multi-functional capabilities for human assistance and augmentation.