The coronavirus disease 2019 (COVID-19) pandemic has immensely disrupted health care services globally. The pandemic has been particularly disruptive for cancer services and more so in low-resource settings. In this narrative review, we highlight the reported impact of the COVID-19 pandemic on cancer prevention, screening, diagnosis, treatment and research across the African continent. We also explore ways in which identified structural and contextual constraints can be navigated for the re-escalation of oncological activities, while discussing how the pandemic has necessitated the reimagination of how oncology services can be delivered now and in the future. We conducted a literature search of MEDLINE (via PubMed) and Scopus for relevant articles and synthesised the findings thematically. In spite of the dearth of data, available evidence suggests a substantial impact of the pandemic on the various aspects of cancer management in African countries. Aggravating factors include pre-existing health system and cancer management gaps in many countries within the region, which are typically faced with inadequate availability of oncology resources, oncologists and other vital resources; in addition to the acute and lingering consequences of social distancing, movement restrictions and other public health measures implemented to contain the spread of the virus. As the pandemic evolves and movement restrictions are eased, there is a need for the timely and safe return to normal oncological care. This will require a risk-adjusted and multidisciplinary approach, with the aim of mitigating the further impact of the disruption on cancer patients, their families and healthcare providers.