The aims of the present study were (1) to determine the differences in body composition and the physical and physiological profile of handball youths across age categories, and (2) to analyze the mediation effect of different categories on the relationship between lean mass or fat mass and specific physical handball capacities. Fifty-four young handball players aged 13 to 18 were assigned to U14 (13- and 14-year-olds), U16 (15- and 16-year-olds), and U18 (17- and 18-year-olds). Body composition was measured using multi-frequency bioelectrical impedance (Inbody®, 230). Handball physical fitness was assessed using handgrip force, jumping tests (squat jump, countermovement jump, countermovement jump with aimed arms), a 30-m sprint, a change-of-direction test (T-half agility test and modified Illinois test), and a Yo-Yo intermittent recovery test level 1. Simple mediation analysis was performed to analyze whether the category mediated the relationship between lean mass or fat mass and physical capacities. No significant differences were observed according to category for the majority of the measured parameters, except for height, lean body mass, and arm span. Lean body mass increased significantly as player category increased (p < 0.05; ∆ = 4.66–9.38; effect size (ES) = 0.96–1.92). The increase in handball category enhanced the majority of the physical capacities evaluated; however, these differences were reduced between the U16 vs. U18 categories. The indirect mediation effect suggests that handball category mediated the relationship between lean mass and upper and lower strength, velocity, agility, and cardiorespiratory fitness. In contrast, an indirect effect suggests that category mediated the relationship between fat mass only in agility and cardiorespiratory fitness. We conclude that U18s showed better body composition parameters, as well as better physical performance scores. Handball category clearly mediated the relationship between body composition through lean mass and fat mass and the physiological profile in handball youth, but lean mass proved to be more relevant when mediating physical performance.