Numerous proteomic and transcriptomic studies have been carried out to better understand the current multi-variant SARS-CoV-2 virus mechanisms of action and effects. However, they are mostly centered on mRNAs and proteins. The effect of the virus on human post-transcriptional regulatory agents such as microRNAs (miRNAs), which are involved in the regulation of 60% of human gene activity, remains poorly explored. Similar to research we have previously undertaken with other viruses such as Ebola and HIV, in this study we investigated the miRNA profile of lung epithelial cells following infection with SARS-CoV-2. At the 24 and 72 h post-infection time points, SARS-CoV-2 did not drastically alter the miRNome. About 90% of the miRNAs remained non-differentially expressed. The results revealed that miR-1246, miR-1290 and miR-4728-5p were the most upregulated over time. miR-196b-5p and miR-196a-5p were the most downregulated at 24 h, whereas at 72 h, miR-3924, miR-30e-5p and miR-145-3p showed the highest level of downregulation. In the top significantly enriched KEGG pathways of genes targeted by differentially expressed miRNAs we found, among others, MAPK, RAS, P13K-Akt and renin secretion signaling pathways. Using RT-qPCR, we also showed that SARS-CoV-2 may regulate several predicted host mRNA targets involved in the entry of the virus into host cells (ACE2, TMPRSS2, ADAM17, FURIN), renin–angiotensin system (RAS) (Renin, Angiotensinogen, ACE), innate immune response (IL-6, IFN1β, CXCL10, SOCS4) and fundamental cellular processes (AKT, NOTCH, WNT). Finally, we demonstrated by dual-luciferase assay a direct interaction between miR-1246 and ACE-2 mRNA. This study highlights the modulatory role of miRNAs in the pathogenesis of SARS-CoV-2.