(1) Background: Drug repositioning is an unconventional drug discovery approach to explore new therapeutic benefits of existing drugs. Currently, it emerges as a rapid avenue to alleviate the COVID-19 pandemic disease. (2) Methods: Herein, we tested the antiviral activity of anti-microbial and anti-inflammatory Food and Drug Administration (FDA)-approved drugs, commonly prescribed to relieve respiratory symptoms, against Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), the viral causative agent of the COVID-19 pandemic. (3) Results: Of these FDA-approved antimicrobial drugs, Azithromycin, Niclosamide, and Nitazoxanide showed a promising ability to hinder the replication of a SARS-CoV-2 isolate, with IC50 of 0.32, 0.16, and 1.29 µM, respectively. We provided evidence that several antihistamine and anti-inflammatory drugs could partially reduce SARS-CoV-2 replication in vitro. Furthermore, this study showed that Azithromycin can selectively impair SARS-CoV-2 replication, but not the Middle East Respiratory Syndrome Coronavirus (MERS-CoV). A virtual screening study illustrated that Azithromycin, Niclosamide, and Nitazoxanide bind to the main protease of SARS-CoV-2 (Protein data bank (PDB) ID: 6lu7) in binding mode similar to the reported co-crystalized ligand. Also, Niclosamide displayed hydrogen bond (HB) interaction with the key peptide moiety GLN: 493A of the spike glycoprotein active site. (4) Conclusions: The results suggest that Piroxicam should be prescribed in combination with Azithromycin for COVID-19 patients.