Objective The COVID-19 pandemic is rapidly spreading worldwide, notably in Europe and North America where obesity is highly prevalent. The relation between obesity and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) has not been fully documented. Methods This retrospective cohort study analyzed the relationship between clinical characteristics, including BMI, and the requirement for invasive mechanical ventilation (IMV) in 124 consecutive patients admitted in intensive care for SARS-CoV-2 in a single French center. Results Obesity (BMI > 30) and severe obesity (BMI > 35) were present in 47.6% and 28.2% of cases, respectively. Overall, 85 patients (68.6%) required IMV. The proportion of patients who required IMV increased with BMI categories (P < 0.01, χ2 test for trend), and it was greatest in patients with BMI > 35 (85.7%). In multivariate logistic regression, the need for IMV was significantly associated with male sex (P < 0.05) and BMI (P < 0.05), independent of age, diabetes, and hypertension. The odds ratio for IMV in patients with BMI > 35 versus patients with BMI < 25 was 7.36 (1.63-33.14; P = 0.02). Conclusions The present study showed a high frequency of obesity among patients admitted in intensive care for SARS-CoV-2. Disease severity increased with BMI. Obesity is a risk factor for SARS-CoV-2 severity, requiring increased attention to preventive measures in susceptible individuals.