We have previously identified methylene blue, a tricyclic phenothiazine dye approved for clinical use for the treatment of methemoglobinemia and used for other medical applications, as a small-molecule inhibitor of the protein-protein interaction (PPI) between the spike protein of the SARS-CoV-2 coronavirus and ACE2, the first critical step of the attachment and entry of this coronavirus responsible for the COVID-19 pandemic. Here, we show that methylene blue concentration-dependently inhibits this PPI for the spike protein of the original strain as well as for those of variants of concerns such as the D614G mutant and delta (B.1.617.2) with IC50 in the low micromolar range (1-5 μM). Methylene blue also showed promiscuous activity and inhibited several other PPIs of viral proteins (e.g., HCoV-NL63 - ACE2, hepatitis C virus E - CD81) as well as others (e.g., IL-2 - IL-2Rα) with similar potency. This non-specificity notwithstanding, methylene blue inhibited the entry of pseudoviruses bearing the spike protein of SARS-CoV-2 in hACE2-expressing host cells both for the original strain and the delta variant. It also blocked SARS-CoV-2 (B.1.5) virus replication in Vero E6 cells with an IC50 in the low micromolar range (1.7 μM) when assayed using quantitative PCR of the viral RNA. Thus, while it seems to be a promiscuous PPI inhibitor with low micromolar activity and it has a relatively narrow therapeutic index, methylene blue inhibits entry and replication of SARS-CoV-2, including several of its mutant variants, and has potential as a possible inexpensive, broad-spectrum, orally bioactive small-molecule antiviral for the prevention and treatment of COVID-19.