Background: The main objective of this research was to analyze whether there were changes in the use of antidepressants, anxiolytics, and hypnotic-sedative drugs, in the context of primary health care, during the COVID-19 pandemic compared to the pre-pandemic period. We further sought to study consumption in vulnerable population groups. Methods: A cross-sectional observational study was performed in a primary health district of Spain. The data were obtained from the Andalusian Public Health System database, for the pre-COVID-19 period, from March 2019 to February 2020, and for the COVID-19 period, from March 2020 to February 2021. Univariant and bivariant analyses were performed. The effect size was measured using the Rosenthal test. Results: While the total number of medical prescriptions decreased by 2.5% in the COVID-19 period, the prescriptions of psychiatric drugs increased by 6.1%. The increase in the dose consumption per 1000 inhabitants (DHD) was highest for anxiolytics (7.2%), followed by hypnotic-sedatives (5.6%) and antidepressants (3.7%). The consumption of antidepressants, anxiolytics, and sedative-hypnotic drugs was higher in women, older people, and rural areas and lower in areas with social transformation needs, with these differences being statistically significant. Conclusions: The consumption of psychiatric drugs has increased over the COVID-19 pandemic, especially in women, older people, and rural areas. Thus, we should reflect on the adequate use of these drugs.