The pandemic caused by the 2019 new coronavirus disease (COVID-19) is harming people's health and well-being all across the world. Scientific literature is progressively reporting on the psychological effects of this epidemic in addition to its effects on physical health, the economy, and society. The research publications on the epidemiology of mental health issues in COVID-19 were the basis for this narrative evaluation. According to recent research, COVID-19 survivors may experience a high burden of mental health issues, such as depression, anxiety disorders, stress, panic attacks, irrational anger, impulsivity, somatization disorder, sleep disorders, emotional disturbance, posttraumatic stress symptoms, and suicidal ideation. Additionally, a number of variables are linked to mental health issues in COVID-19, including age, gender, marital status, education, occupation, income, area of residence, coexisting physical and mental health issues, exposure to news and social media about COVID-19, coping mechanisms, stigma, psychological support, health communication, trust in health systems, personal protective measures, and perceived chance of survival. Additionally, there were differences in the epidemiological distribution of mental health issues and related factors among the general public, COVID-19 patients, and healthcare professionals. The COVID-19 pandemic and a psychiatric epidemic appear to be co-occurring, according to the available information, which requires the attention of the international health community. Future epidemiological research should focus on the varying psychopathologies and the temporality of mental health issues in various communities. However, in order to address the current psychological issues and advance mental health in the context of the COVID-19 epidemic, multifaceted treatments should be created and implemented.