Background: The COVID-19 pandemic had profound impacts worldwide on individuals with mental and behavioral disorders, including disorders due to psychoactive substance use. We investigated how the COVID-19 pandemic affected the trends in these disorders in the Republic of Kazakhstan. Methods: We researched and compared ICD-10 data on mental and behavioral disorders due to substance use in Kazakhstan that were diagnosed in 2018–2019 (pre-pandemic) versus 2020–2021 (the pandemic period). Results: The data for the pandemic period were significantly different from those of the pre-pandemic in that (i) ‘other stimulant-related disorders (F15)’ and ‘other psychoactive substance-related disorders (F19)’ were increased in the younger age groups, (ii) the risk of ‘opioid-related disorders (F11)’ was decreased in the 30-year-old group in both males and females, and (iii) the risk of ‘alcohol-related disorders (F10)’ was increased in the 30-year-old group and decreased in the 20- and 50-year-old groups. In only the males, (iv) the risk of ‘other psychoactive substance-related disorders (F19)’ was increased in almost all of the age groups, and (v) the risk of ‘cannabis-related disorders (F12)’ was increased in the ≥50-year-olds. The pre-pandemic and pandemic periods thus involved changes due to COVID-19 in both males and females that were especially notable in males. Conclusions: These results indicate that further measures designed to prevent mental and behavioral disorders due to psychoactive substances are necessary at the primary, secondary, and tertiary levels, and personnel in medicine/nursing, the government, private organizations, and the public need to collaborate to devise such measures.