In patients with cancer, tumor- and treatment-induced immunosuppression are responsible for a four-fold increase in morbidity and mortality caused by influenza and invasive Streptococcus pneumoniae infections compared to the general population. The main oncology societies strongly recommend vaccination in patients with cancer to prevent these infections. However, vaccine hesitancy is a main concern in this population. The aim of this study was to assess the feasibility of in-hospital vaccination for patients under anticancer treatment and their family members (FMs) against influenza and pneumococcal infections during the COVID-19 pandemic in order to increase vaccine coverage. This was a single-center, prospective, observational study conducted at the Department of Oncology of Luigi Sacco University Hospital (Milan, Italy) between October 2020 and April 2021. The main primary outcome was the incidence of influenza-like illness (ILI) and pneumococcal infections. The main secondary outcome was safety. A total of 341 subjects were enrolled, including 194 patients with cancer and 147 FMs. The incidence of ILI was higher among patients than among FMs (9% vs. 2.7%, OR 3.92, p = 0.02). Moreover, two subjects were diagnosed with pneumococcal pneumonia. The most frequent vaccine-related AEs were pain in the injection site (31%) and fatigue (8.7%). In conclusion, this hospital-based vaccination strategy was feasible during the COVID-19 pandemic, representing a potential model to maximize vaccine coverage during a public health emergency.