The functionality and natural motion of prosthetic hands remain limited by the challenges in controlling compliant wrist mechanisms. Current control strategies often lack adaptability and incur high computational costs, which impedes real-time deployment in assistive robotics. To address this gap, this study presents a computationally efficient Neural Network (NN)-based Model Reference Adaptive Controller (MRAC) for a tendon-driven soft continuum wrist integrated with a prosthetic hand. The dynamic modeling of the wrist is formulated using Timoshenko beam theory, capturing both shear and bending deformations. The proposed NN-MRAC estimates the required tendon forces from deflection errors and minimizes deviation from a reference model through online adaptation. Simulation results demonstrate improved precision with a root mean square error (RMSE) of \(6.14 \times 10^{-4}\) m and a settling time of 3.2 s. Experimental validations confirm real-time applicability, with an average RMSE of \(5.66 \times 10^{-3}\) m, steady-state error of \(8.05 \times 10^{-3}\) m, and settling time of 1.58 s. These results highlight the controller’s potential to enhance motion accuracy and responsiveness in soft prosthetic systems, thereby advancing the integration of adaptive intelligent control in wearable assistive devices.