Background: Emerging evidence suggests that the COVID-19 pandemic is widening pre-pandemic health, social, and economic inequalities between refugees, migrants, and asylum seekers and the general population. This global scoping review examined the impact of the pandemic on community-based asylum seekers and undocumented migrants in high- and upper-middle-income countries. Methods: We conducted a systematic search of peer-reviewed articles in PubMed, Scopus, Web of Science, and ProQuest Central. We applied Katikireddi’s framework of understanding and addressing inequalities to examine the differential impact of the pandemic across exposure, vulnerability to infection, disease consequences, social consequences, effectiveness of control measures, and adverse consequences of control measures. Results: We included 32 articles in the review. The analysis showed that asylum seekers and undocumented migrants experienced greater exposure to the COVID-19 virus and higher infection rates. They also experienced differential social consequences in the form of job loss and lost and/or reduced work hours. The effectiveness of pandemic response measures on asylum seekers and undocumented migrants was also affected by pre-pandemic social and economic marginalisation, exclusion from pandemic-induced policy measures, lack of appropriate pandemic communication, and variable trust in governments and authority. Pandemic control measures had greater adverse consequences on asylum seekers and undocumented migrants than the general population, with the majority of studies included in this review reporting worsened mental health and social isolation conditions and reduced access to health care. Conclusions: Asylum seekers and undocumented migrants experienced a disproportionate impact of the COVID-19 pandemic across the six thematic areas of comparison. Policies that reduce exposure and vulnerability to the infection, grant equitable access to health and social care, and build capacities and resilience, are critical to enable asylum seekers and undocumented migrants to cope with and recover from pre-pandemic and pandemic-induced inequalities.