The human hand comprises complex sensorimotor functions that can be impaired by neurological diseases and traumatic injuries. Effective rehabilitation can bring the impaired hand back to a functional state because of the plasticity of the central nervous system to relearn and remodel the lost synapses in the brain. Current rehabilitation therapies focus on strengthening motor skills, such as grasping, employ multiple objects of varying stiffness so that affected persons can experience a wide range of strength training. These devices have limited range of stiffness due to the rigid mechanisms employed in their variable stiffness actuators. This paper presents a novel soft robotic haptic device for neuromuscular rehabilitation of the hand, which is designed to offer adjustable stiffness and can be utilized in both clinical and home settings. The device eliminates the need for multiple objects by employing a pneumatic soft structure made with highly compliant materials that act as the actuator of the haptic interface. It is made with interchangeable sleeves that can be customized to include materials of varying stiffness to increase the upper limit of the stiffness range. The device is fabricated using existing 3D printing technologies, and polymer molding and casting techniques, thus keeping the cost low and throughput high. The haptic interface is linked to either an open-loop system that allows for an increased pressure during usage or closed-loop system that provides pressure regulation in accordance to the stiffness the user specifies. Preliminary evaluation is performed to characterize the effective controllable region of variance in stiffness. It was found that the region of controllable stiffness was between points 3 and 7, where the stiffness appeared to plateau with each increase in pressure. The two control systems are tested to derive relationships between internal pressure, grasping force exertion on the surface, and displacement using multiple probing points on the haptic device. Additional quantitative evaluation is performed with study participants and juxtaposed to a qualitative analysis to ensure adequate perception in compliance variance. The qualitative evaluation showed that greater than 60% of the trials resulted in the correct perception of stiffness in the haptic device.