Background: Understanding the effects of the COVID-19 pandemic on cause-specific mortality should be a priority, as this metric allows for a detailed analysis of the true burden of the pandemic. The aim of this systematic literature review is to estimate the impact of the pandemic on different causes of death, providing a quantitative and qualitative analysis of the phenomenon. Methods: We searched MEDLINE, Scopus, and ProQuest for studies that reported cause-specific mortality during the COVID-19 pandemic, extracting relevant data. Results: A total of 2413 articles were retrieved, and after screening 22 were selected for data extraction. Cause-specific mortality results were reported using different units of measurement. The most frequently analyzed cause of death was cardiovascular diseases (n = 16), followed by cancer (n = 14) and diabetes (n = 11). We reported heterogeneous patterns of cause-specific mortality, except for suicide and road accident. Conclusions: Evidence on non-COVID-19 cause-specific deaths is not exhaustive. Reliable scientific evidence is needed by policymakers to make the best decisions in an unprecedented and extremely uncertain historical period. We advocate for the urgent need to find an international consensus to define reliable methodological approaches to establish the true burden of the COVID-19 pandemic on non-COVID-19 mortality.