Background: The risk factors for developing a severe form of COVID-19 in young children are poorly understood. Methods: A single-center retrospective study was conducted to quantify and analyze the clinical risk profile of children admitted to the Pediatric Clinic for Nutritional Recovery. Results: Overall, 51.5% (n = 17) of children were infected with SARS-CoV-2, all symptomatic, and five of them (29.4%) developed a severe form. A positive clinical pulmonary exam was only associated with the severe outcome (OR: 2.00; 95% CI, 0.33–5.66; p = 0.02). Other factors such as age under 3 months, prematurity, birth weight, malnutrition or positive history of congenital cardiac, neurodevelopmental, or genetic diseases, fever, temperature, cough, and digestive symptoms were not found to be significant risk factors. Conclusions: Clinical guidelines based on risk stratification for SARS-CoV-2 infection in children are needed in order to manage, monitor and establish priority access for some groups to high medical care.