Handball players are at a high risk of suffering a sport-related injury. Recent studies in various adult populations (e.g., US Army soldiers/warrior athletes, and military members) showed that poor scores in the upper quarter Y-balance test (YBT-UQ) are related to an increased risk of injury. Yet, it is unclear whether this also applies to adolescent handball players. Thus, the present study aims to determine if pre-season YBT-UQ performance is associated with sport-related injuries during the competitive season in adolescent handball players. One hundred and thirty-three adolescent handball players (age: 15.4 ± 1.7 years; m = 99, f = 42) who competed in the second highest league in the Rhine-Ruhr region, Germany, during the 2021/2022 season participated in the study. Before the competitive season, the players performed the YBT-UQ to assess upper extremity mobility and stability of the throwing and non-throwing arm. Over the 8-month competitive season, the coaches monitored the occurrence of sports-related injuries once a week, using an injury report form from the legal accident insurance. Fifty-seven players (43%) incurred a sport-related injury during the competitive season, of which 27 (47%) had upper body injuries, and 30 (53%) were lower body injuries. The YBT-UQ performance of the throwing and non-throwing arm did not significantly differ between injured and non-injured players. Further, Cox proportional hazard survival regression model analyses revealed that only the presence of an inferolateral reach asymmetry score ≥7.75% arm length was associated with a moderate increase in the risk (hazard ratio = 2.18, 95% confidence interval = 1.02–4.68, p = 0.045) of lower but not upper or whole-body injuries. Our findings suggest that the YBT-UQ has limited value as a field-based screening tool to assess the risk of sport-related injuries in adolescent handball players.