Background: The objective of this review was to identify and synthesize the findings of the existing literature that highlighted the psychosocial and mental health issues of the migrants during the COVID-19 pandemic in India. Materials and Methods: An exploration of the PubMed, Google Scholar, Web of Science, ScienceDirect, Google search, and some other manual searches was undertaken so that no relevant study was missed. A search on Indian scientific literature and cross-references retrieved was also conducted to get further information. The period of the search has been one year from March 1, 2020, to March 31, 2021. The database was searched with the terms “migrants,” “migrant workers,” “COVID-19 pandemic,” “lockdown,” “migrant population,” “mental health issues,” “psychosocial issues” to retrieve the published literature. Results: Initially, 48 research articles were retrieved and 10 of them were excluded as they had no sufficient information about mental and psychosocial challenges faced by the migrants. In the remaining 38 articles, 9 articles were original research work ( n = 9) published from India related to the impact of COVID-19 on migrants. The second category consisted of editorials or commentary or letters to the editor or policy paper on psychosocial and mental health aspects of migrants during the COVID-19 pandemic ( n = 17). The third category was 11 articles on perspectives or opinions or viewpoints ( n = 11) related to various psychosocial and mental health issues among migrants in India during the COVID-19 pandemic. Predominantly psychosocial issues found among migrants were living conditions, basic needs, family concerns, and joblessness. The mental health issues found among migrants during the COVID-19 pandemic included psychological distress, depressive disorders, anxiety disorders, substance use disorders. Conclusion: Existing literature from India has shown that the COVID-19 pandemic severely impacted the psychosocial and mental health status of the migrants in India. This review suggests the need for more research work from the affected states of India and the development of psychosocial and mental health intervention strategies to minimize the impact of the COVID-19 pandemic on migrants.