Considering cancer patients may be at an increased risk of severe COVID-19 disease, their oncologic treatment cannot be delayed without risking their oncologic outcomes. Considering this, a comprehensive evaluation is required for the management of malignant diseases such as melanoma. The current study aimed to assess the impact of the COVID-19 pandemic on the delivery of cancer care services for patients diagnosed with malignant melanoma in Romania; to document the difference in patients’ addressability and melanoma staging between the pandemic and pre-pandemic periods; as well as to determine the risk factors responsible for disease progression during the pandemic. We developed a retrospective analysis using a monocentric hospital database to compare the final 24 months of the pre-pandemic era to the first 24 months of the COVID-19 pandemic. All outpatients and inpatients with a diagnosis of malignant melanoma were screened during the study period and included in the analysis if matching the inclusion criteria. A total of 301 patients were included in the study, with 163 cases identified in the 24 months before the COVID-19 pandemic and 138 patients during the first 24 months of the pandemic. It was observed during the first two lockdown periods from March to May 2020, and, respectively, from October to December 2020, that significantly fewer patients with malignant melanoma presented for specialized medical care, while there was a statistically significantly lower proportion of outpatients due to COVID-19 restrictions (18.1% vs. 42.9%). The average Breslow depth was 1.1 mm before the pandemic, compared with 1.8 mm during the pandemic (p-value < 0.001). Third-stage patients were the most prevalent during both study periods, although with a statistically significant difference during the pandemic, with an increase from 90 (55.2%) patients to 94 (68.1%) (p-value < 0.001). The significant risk factors for disease progression were advanced AJCC stage (HR = 3.48), high Breslow index (HR = 3.19), postponed treatment (HR = 2.46), missed appointments (HR = 2.31), anemia at presentation (HR = 1.60), and patient’s age (HR = 1.57). After the pandemic limitations are brought to an end, a broad skin-cancer-screening campaign is warranted to detect the missed cases during COVID-19.