Handball demands intense movements like rapid direction changes and physical contact. Consecutive competitions expose player fatigue and weaknesses due to the sport’s exhaustive nature. Therefore, the aims of this study are twofold: (i) to investigate the impact of competitive fatigue on the body composition of youth elite handball players, and (ii) to analyze the impact of concentrated competition on their functional capacity performance. Seventeen young male handball players (age: 16.2 years, height; 177.8 cm, body mass: 73.0 kg) were assessed twenty-four hours before (TM1) and after the competitive period (TM2) in body composition, static strength, lower- and upper-body explosive strength, speed, agility, balance, and flexibility indicators. A Wilcoxon Signed Rank Test was conducted to assess differences in body composition and functional capacities assessment between TM1 and TM2. Regarding results, body mass significantly increased in TM2 (p < 0.01), while increases in waist circumference and body fat percentage were not statistically significant. Functional capacity assessments revealed a significant decline in jumping performance (CMJ and SJ; p ≤ 0.01). Speed and agility assessments showed worse performance in TM2, significantly increasing 30 m sprint time (p ≤ 0.01). Balance indicators showed no significant differences, with mixed results in performance across different conditions. In sum, evaluating vertical jumps and long-distance maximum speed (i.e., 30 meters) could be valid tests for measuring and controlling fatigue in young elite handball players. Future research should regularly monitor young handballers after the competition to analyze the entire fatigue recovery process.