Background: The pandemic had a strong impact on healthcare for other diseases, the so-called collateral damage. This situation heavily impacted the health care system, causing a deferment of surgical admissions. This situation had an immediate and long-term impact on millions of patients with surgical diseases all over the world. The objective of this study was to evaluate the incidence of hospitalizations for colorectal and breast cancers in an Italian region during 2020 and to compare it with years 2018–2019. Methods: This retrospective study was performed in the Abruzzo region, Italy. All admissions occurred during years 2018-20 for colorectal and breast cancers were considered. Data were extracted from hospital discharge records. Monthly number of hospitalizations for both diseases in the year 2020 was compared with a control period consisting of the average of admissions that occurred in the years 2018–2019 using Poisson regression. Results: In the Abruzzo region, during the year 2020, a total of 604 patients were admitted for colorectal cancer surgery, and 1012 patients were admitted for breast cancer surgery. A reduction in hospital admissions for all diseases considered was found. In particular, compared with years 2018–2019, admissions for colorectal cancer were 35.71% lower (HRR 0.915; 95% CI: 0.914–0.916; p < 0.001), and admissions for breast cancer were 10.36% lower (HRR 0.895; CI: 0.894–0.897; p < 0.001). Considering the monthly incidence of hospitalization, a significant reduction was observed particularly between March and June 2020, and during the last two months of the year 2020, for both cancers compared to previous years. Conclusions: The results of this study showed the impact of the COVID-19 pandemic on surgery volume for two common oncological surgeries. These results highlighted the need of strategic measures to deal with new cancer diagnoses and surgery overload during the coming years.