The rapid spread of COVID-19 overwhelmed existing health care systems, finding it challenging to provide essential health services besides the COVID-19 response interventions. Refugees are disproportionately affected by the COVID-19 pandemic because of the barriers they face to access health care. However, there is limited research investigating how access to HIV/AIDS or TB care services by urban refugees is affected during pandemics such as the COVID-19. This study adopted a cross-sectional survey among urban refugees living in Kampala, Uganda. Results offer major insights into the effect of COVID-19 control measures on disruption of access to services particularly in relation to being able to access service points. The findings suggest recognizing structural barriers to uninterrupted or continued access to HIV/AIDS or TB services during pandemics such as COVID-19 can help stakeholders to design measures that make it possible for more urban refugees to access HIV/AIDS or TB services.