The pandemic is aggravating health inequalities, particularly mental health inequalities, while revealing the social determinants of these inequalities, including migration as a social determinant that mediates the interaction of social, economic, cultural, institutional, and structural factors with health indicators. Therefore, it is of most relevance to identify the multiple interconnected factors that influence the mental health and well-being of migrant populations. A scoping review was developed to map the research performed in this area and to identify any gaps in knowledge, following the PRISMA extension for scoping reviews. MEDLINE, Scopus, and WHO Global Health research databases on COVID-19 were searched from January 2020 to October 2021. The review followed the inclusion criteria Population/Concept/Context (PCC): Population-Adult International migrants (including refugees, asylum seekers, and undocumented migrants); Concept-determinants of (and factors influencing) mental health and well-being; Context-COVID-19 anywhere in the world. Of the sixty-five selected studies, eleven were from European countries and were the focus of this review with special attention to health inequalities experienced by migrants in Europe. The results cover a diversity of themes related to the effects of COVID-19 on the mental health of migrants (country-level environmental factors, social determinants of mental health, mental health indicators and outcomes), responses (such as solidarity and resilience), populations, and study methods. The evidence found can inform recommendations and interventions focused on health promotion and mitigation of the inequalities accentuated by the pandemic.