Handball is a team sport that involves fourteen players who are attempting to score more goals than their opponent within two thirty-minute halves. A biomechanical analysis based on measuring the kinematics of jump throws could provide us with information on the ball’s velocity, the maximal internal rotation of the trunk, and the trunk’s flexion, as well as the angular velocity of the ball during shoulder rotation. The main aim of this study was to determine the wrist velocity during jump throws and standing throws without a run-up. The trunk, arm rotation, and wrist velocity will influence the speed of the ball during throwing. This case study included a senior-grade male handball player aged 18.75 years with a body mass index (BMI) of 25.5. The biomechanical evaluation was carried out using a three-dimensional Vicon system. The biomechanical analysis consisted of an evaluation of angular trunk velocity, angular arm rotation velocity, and wrist velocity during two types of throwing: jump throws and standing throws without a run-up. The data were recorded for standing throws without a run-up (S1) and jump throws (S2). For each situation, we measured two phases due to the great variation in the kinematic parameters. Phase 1 (F1) occurred when the elbow angle was 90°, up to the moment when the wrist had an inflection of its trajectory, and Phase 2 (F2) finished when the wrist’s velocity reached its maximum. The results regarding the angular velocity of the trunk torsion showed a high value of this parameter during Phase F2 compared to Phase F1 for both types of throws (S1 and S2). The angular velocity of the arm rotation achieved its maximum value in F2 during S2, and the wrist velocity was highest during Phases F2 and S2. The correlation analysis demonstrated that there was a good correlation between the angular velocity of the trunk torsion and the angular velocity of the arm rotation for S1 in Phase F1; however, in Phase F2, we found a good correlation between the angular velocity of the trunk torsion and wrist velocity. For S2, we found that in Phase F1, there was a good correlation between the angular velocity of the trunk torsion and wrist velocity; however, for Phase F2, there was a good correlation between the angular velocity of the arm’s rotation and wrist velocity. Therefore, the results from this case study indicate that the wrist velocity is influenced by the other two kinematic parameters, especially the angular velocity of the arm’s rotation. This means that the development of explosive force in the muscles of the trunk and arm could improve the wrist’s velocity and also increase the optimization of throwing in handball.