This paper presents a robust approach for enhancing Human-Robot Interaction (HRI) through short-term human hand motion prediction, enabling robots to better anticipate human intentions in shared spaces. By leveraging real-time body tracking for monitoring human motion, the system integrates model-based hand path generation into a Bayesian inference framework to predict reaching goals. Incorporating both hand and shoulder data, the approach improves the accuracy and responsiveness of the proposed Bayesian recursive classifier, supporting seamless and intuitive collaboration. A comprehensive testing phase using offline tracking data demonstrates the method’s superior performance compared to state-of-the-art approaches. A collaborative assembly use case designed to validate the applicability and effectiveness of the approach in a real-world setting further demonstrated increased efficiency and fluency in HRI. By enabling robots to interpret and reactively respond to fast-changing human intentions in real-time, this research contributes to the advancement of social robotics, promoting natural and effective interactions in various contexts, such as domestic assistance, healthcare, and industrial environments, where trust, timing, and coordination are key to successful human-robot teamwork.