Since December 2019, the world has been devastated by the Coronavirus Disease 2019 (COVID-19) pandemic. Emergency Departments have been experiencing situations of urgency where clinical experts, without long experience and mature means in the fight against COVID-19, have to rapidly decide the most proper patient treatment. In this context, we introduce an artificially intelligent tool for effective and efficient Computed Tomography (CT)-based risk assessment to improve treatment and patient care. In this paper, we introduce a data-driven approach built on top of volume-of-interest aware deep neural networks for automatic COVID-19 patient risk assessment (discharged, hospitalized, intensive care unit) based on lung infection quantization through segmentation and, subsequently, CT classification. We tackle the high and varying dimensionality of the CT input by detecting and analyzing only a sub-volume of the CT, the Volume-of-Interest (VoI). Differently from recent strategies that consider infected CT slices without requiring any spatial coherency between them, or use the whole lung volume by applying abrupt and lossy volume down-sampling, we assess only the "most infected volume" composed of slices at its original spatial resolution. To achieve the above, we create, present and publish a new labeled and annotated CT dataset with 626 CT samples from COVID-19 patients. The comparison against such strategies proves the effectiveness of our VoI-based approach. We achieve remarkable performance on patient risk assessment evaluated on balanced data by reaching 88.88%, 89.77%, 94.73% and 88.88% accuracy, sensitivity, specificity and F1-score, respectively.