Effective prioritization plays critical roles in precision medicine. Healthcare decisions are complex, involving trade-offs among numerous frequently contradictory priorities. Considering the numerous difficulties associated with COVID-19, approaches that could triage COVID-19 patients may help in prioritizing treatment and provide precise medicine for those who are at risk of serious disease. Prioritizing a patient with COVID-19 depends on a variety of examination criteria, but due to the large number of these biomarkers, it may be hard for medical practitioners and emergency systems to decide which cases should be given priority for treatment. The aim of this paper is to propose a Multidimensional Examination Framework (MEF) for the prioritization of COVID-19 severe patients on the basis of combined multi-criteria decision-making (MCDM) methods. In contrast to the existing literature, the MEF has not considered only a single dimension of the examination factors; instead, the proposed framework included different multidimensional examination criteria such as demographic, laboratory findings, vital signs, symptoms, and chronic conditions. A real dataset that consists of data from 78 patients with different examination criteria was used as a base in the construction of Multidimensional Evaluation Matrix (MEM). The proposed framework employs the CRITIC (CRiteria Importance Through Intercriteria Correlation) method to identify objective weights and importance for multidimensional examination criteria. Furthermore, the VIKOR (VIekriterijumsko KOmpromisno Rangiranje) method is utilized to prioritize COVID-19 severe patients. The results based on the CRITIC method showed that the most important examination criterion for prioritization is COVID-19 patients with heart disease, followed by cough and nasal congestion symptoms. Moreover, the VIKOR method showed that Patients 8, 3, 9, 59, and 1 are the most urgent cases that required the highest priority among the other 78 patients. Finally, the proposed framework can be used by medical organizations to prioritize the most critical COVID-19 patient that has multidimensional examination criteria and to promptly give appropriate care for more precise medicine.