Technological advances in multi-articulated prosthetic hands have outpaced the development of methods to intuitively control these devices. In fact, prosthetic users often cite "difficulty of use" as a key contributing factor for abandoning their prostheses. To overcome the limitations of the currently pervasive myoelectric control strategies, namely unintuitive proportional control of multiple degrees-of-freedom, we propose a novel approach: proprioceptive sonomyographic control. Unlike myoelectric control strategies which measure electrical activation of muscles and use the extracted signals to determine the velocity of an end-effector; our sonomyography-based strategy measures mechanical muscle deformation directly with ultrasound and uses the extracted signals to proportionally control the position of an end-effector. Therefore, our sonomyography-based control is congruent with a prosthetic user's innate proprioception of muscle deformation in the residual limb. In this work, we evaluated proprioceptive sonomyographic control with 5 prosthetic users and 5 able-bodied participants in a virtual target achievement and holding task for 5 different hand motions. We observed that with limited training, the performance of prosthetic users was comparable to that of able-bodied participants and thus conclude that proprioceptive sonomyographic control is a robust and intuitive prosthetic control strategy.