The association between younger age and poorer mental health during the COVID-19 pandemic has been documented. Whether these changes were associated with a change in antidepressant (AD) use is not well understood. This study aimed to estimate the impact of the COVID-19 pandemic on AD use by young adults in the ASL TO4 Regione Piemonte (Italy). The impact of the pandemic on the weekly prevalence of AD users was assessed using interrupted time-series analysis with autoregressive integrated moving average models. A total of 1071 subjects (18–22 years with ≥1 AD dispensation) were included in the study. The observed prevalence was lower than the predicted value for several weeks after the introduction of the lockdown. However, it was consistently higher than the predicted values from week 134. The maximum difference between observed and predicted values (25 subjects per 10,000 young adults) was found at week 170. Changes in AD use were observed in both genders and were more pronounced for selective serotonin reuptake inhibitors. In conclusion, the impact of the COVID-19 pandemic on the mental health of young adults is likely to be significant in the coming years, which may place a future burden on pharmaceutical public health and community health.