Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the main cause of COVID-19, causing hundreds of millions of confirmed cases and more than 18.2 million deaths worldwide. Acute kidney injury (AKI) is a common complication of COVID-19 that leads to an increase in mortality, especially in intensive care unit (ICU) settings, and chronic kidney disease (CKD) is a high risk factor for COVID-19 and its related mortality. However, the underlying molecular mechanisms among AKI, CKD, and COVID-19 are unclear. Therefore, transcriptome analysis was performed to examine common pathways and molecular biomarkers for AKI, CKD, and COVID-19 in an attempt to understand the association of SARS-CoV-2 infection with AKI and CKD. Three RNA-seq datasets (GSE147507, GSE1563, and GSE66494) from the GEO database were used to detect differentially expressed genes (DEGs) for COVID-19 with AKI and CKD to search for shared pathways and candidate targets. A total of 17 common DEGs were confirmed, and their biological functions and signaling pathways were characterized by enrichment analysis. MAPK signaling, the structural pathway of interleukin 1 (IL-1), and the Toll-like receptor pathway appear to be involved in the occurrence of these diseases. Hub genes identified from the protein–protein interaction (PPI) network, including DUSP6, BHLHE40, RASGRP1, and TAB2, are potential therapeutic targets in COVID-19 with AKI and CKD. Common genes and pathways may play pathogenic roles in these three diseases mainly through the activation of immune inflammation. Networks of transcription factor (TF)–gene, miRNA–gene, and gene–disease interactions from the datasets were also constructed, and key gene regulators influencing the progression of these three diseases were further identified among the DEGs. Moreover, new drug targets were predicted based on these common DEGs, and molecular docking and molecular dynamics (MD) simulations were performed. Finally, a diagnostic model of COVID-19 was established based on these common DEGs. Taken together, the molecular and signaling pathways identified in this study may be related to the mechanisms by which SARS-CoV-2 infection affects renal function. These findings are significant for the effective treatment of COVID-19 in patients with kidney diseases.