The coronavirus disease 2019 (COVID-19) pandemic causes many morbidity and mortality cases. Despite several developed vaccines and antiviral therapies, some patients experience severe conditions that need intensive care units (ICU); therefore, precision medicine is necessary to predict and treat these patients using novel biomarkers and targeted drugs. In this study, we proposed a multi-level biological network analysis framework to identify key genes via protein–protein interaction (PPI) network analysis as well as survival analysis based on differentially expressed genes (DEGs) in leukocyte transcriptomic profiles, discover novel biomarkers using microRNAs (miRNA) from regulatory network analysis, and provide candidate drugs targeting the key genes using drug–gene interaction network and structural analysis. The results show that upregulated DEGs were mainly enriched in cell division, cell cycle, and innate immune signaling pathways. Downregulated DEGs were primarily concentrated in the cellular response to stress, lysosome, glycosaminoglycan catabolic process, and mature B cell differentiation. Regulatory network analysis revealed that hsa-miR-6792-5p, hsa-let-7b-5p, hsa-miR-34a-5p, hsa-miR-92a-3p, and hsa-miR-146a-5p were predicted biomarkers. CDC25A, GUSB, MYBL2, and SDAD1 were identified as key genes in severe COVID-19. In addition, drug repurposing from drug–gene and drug–protein database searching and molecular docking showed that camptothecin and doxorubicin were candidate drugs interacting with the key genes. In conclusion, multi-level systems biology analysis plays an important role in precision medicine by finding novel biomarkers and targeted drugs based on key gene identification.