Methylene blue has multiple antiviral properties against Severe Acute Respiratory Syndrome-related Coronavirus 2 (SARS-CoV-2). The ability of methylene blue to inhibit different stages of the virus life cycle, both in light-independent and photodynamic processes, is used in clinical practice. At the same time, the molecular aspects of the interactions of methylene blue with molecular components of coronaviruses are not fully understood. Here, we use Brownian dynamics to identify methylene blue binding sites on the SARS-CoV-2 envelope. The local lipid and protein composition of the coronavirus envelope plays a crucial role in the binding of this cationic dye. Viral structures targeted by methylene blue include the S and E proteins and negatively charged lipids. We compare the obtained results with known experimental data on the antiviral effects of methylene blue to elucidate the molecular basis of its activity against coronaviruses.