The critical role played by the nutritional status in the complications, duration of hospitalization and mortality in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection (COVID-19) has emerged from several research studies in diverse populations. Obesity has been associated with an increased risk of serious complications, as the adipose tissue appears to have significant effects on the immune response. The aim of this narrative review was to investigate the relationship between COVID-19 and obesity. We performed a review of papers in the English language derived from PubMed, Science Direct, and Web of Science. The primary outcomes investigated were the severity of the disease, admission to the intensive care unit (ICU), need for intubation, and mortality. Review of 44 eligible studies from 18 countries around the world revealed evidence that obesity increases the risk of severe COVID-19 complications, ICU admission, intubation and mortality. Patients with a higher body mass index (BMI) appear to be more vulnerable to SARS-CoV-2 infection, with more severe illness requiring admission to ICU and intubation, and to have higher mortality. A healthy body weight should be targeted as a long-term prevention measure against acute complications of infection, and in the event of COVID-19, overweight and obese patients should be monitored closely.