In this perspective, we discuss the impact of COVID-19 on tuberculosis (TB)/HIV health services and approaches to mitigating the growing burden of these three colliding epidemics in sub-Saharan Africa (SSA). SSA countries bear significantly high proportions of TB and HIV cases reported worldwide, compared to countries in the West. Whilst COVID-19 epidemiology appears to vary across Africa, most countries in this region have reported relatively lower-case counts compared to the West. Nevertheless, the COVID-19 pandemic has added an additional burden to already overstretched health systems in SSA, which, among other things, have been focused on the longstanding dual epidemics of TB and HIV. As with these dual epidemics, inadequate resources and poor case identification and reporting may be contributing to underestimations of the COVID-19 case burden in SSA. Modelling studies predict that the pandemic-related disruptions in TB and HIV services will result in significant increases in associated morbidity and mortality over the next five years. Furthermore, limited empirical evidence suggests that SARS-CoV-2 coinfections with TB and HIV are associated with increased mortality risk in SSA. However, predictive models require a better evidence-base to accurately define the impact of COVID-19, not only on communicable diseases such as TB and HIV, but on non-communicable disease comorbidities. Further research is needed to assess morbidity and mortality data among both adults and children across the African continent, paying attention to geographic disparities, as well as the clinical and socio-economic determinants of COVID-19 in the setting of TB and/or HIV.