Smooth and responsive motion is critical for physical human-robot interaction and humanoid robotics, where sudden accelerations and jerks can lead to unsafe or unnatural behavior. Traditional Time-Optimal Path Parameterization (TOPP) methods often yield discontinuous acceleration profiles due to abrupt torque transitions, resulting in high jerk and degraded motion quality. In this paper, we propose a novel trajectory optimization framework—Minimized Jerk Time-Optimal Path Parameterization (MJ-TOPP)—that incorporates both torque and jerk constraints to generate interaction-friendly motion. The method introduces a piecewise polynomial optimization scheme around torque switching points, enabling a global reduction in jerk while preserving near-optimal timing. Simulation and experimental results on a 6-DOF robotic manipulator performing a complex “HIT”-shaped trajectory demonstrate that MJ-TOPP reduces peak joint jerk by over 90% with only a 1.25% increase in execution time. Moreover, the improved motion smoothness leads to a 15.4% decrease in average end-effector tracking error, enhancing the safety and stability of robot behavior in human-centered environments. This approach provides a practical and effective solution for compliant motion planning in intelligent, human-interactive robotic systems.