Background: The COVID-19 pandemic has affected children and adolescents in several ways, including worsened mental health, improvement of asthma, and increases in diabetes ketoacidosis. Less is known about how medication use in children and adolescents has been affected by the pandemic. Objectives: To explore how the COVID-19 pandemic affected drug utilisation in children and adolescents in Norway, Sweden, and Italy, by child age. Methods: We conducted a longitudinal drug utilisation study among all children and adolescents (<18 years old) in Norway and Sweden and a nationwide paediatric database covering 3% of the paediatric population in Italy. We conducted an interrupted time-series analysis from January 2018 to December 2021, with March 2020 as the interruption point. Dispensing or prescription rates of antidepressants, anxiolytics, sleep medications, attention-deficit/hyperactivity disorder (ADHD) medications, insulin, and asthma medications were examined. Results: The study population in January 2018 consisted of 3,455,521 children and adolescents (136,188 from Italy, 1,160,431 from Norway, and 2,158,902 from Sweden). For sleep medications and insulin, there were only minor changes in level or trend in some age groups after March 2020. For asthma medications, the pandemic was associated with an immediate decrease in dispensing in Norway and Sweden (range of change in level: −19.2 to −3.7 dispensings per 1000 person-months), and an increasing trend in all countries afterward (range of change in trend: 0.3–6.4 dispensings per 1000 person-months), especially for the youngest age groups. Among adolescents, the pandemic was associated with an increased trend for ADHD medications, antidepressants, and anxiolytics in Norway and Sweden, but not in Italy. Conclusions: The increasing trend of psychotropic medication dispensing, especially among adolescents after the start of the pandemic, is concerning and should be investigated further. Aside from a temporary effect on asthma medication dispensing, the pandemic did not greatly affect the dispensing of the medications investigated.