The wrist can significantly enhance the hand’s dexterity and its ability to manipulate objects. Hence, the design of prosthetic wrists holds significant significance. Nevertheless, currently available prosthetic wrists on the market exhibit issues such as substantial bulk and volume, as well as inadequate torque density. In this paper, we present the structural design and kinematic analysis of a novel three-Degree of Freedom (DoF) parallel prosthetic wrist, which incorporates a Brushless DC motor (BLDC)-ball screw as the actuator-transmission. The proposed prosthetic wrist mimics the physiological and anatomical features of the human wrist and can generate the movements of wrist Flexion/Extension (F/E), Radial/Ulnar Deviation (R/U) and Pronation/Supination (P/S). The mechanism benefits from a compact construction, low weight, and a wide range of motion (RoM) due to the co-linear series arrangement of the motor and ball screw. To verify the feasibility of the mechanism’s motion, we conducted kinematic analysis and simulation.