Bangpungtongsung-san (BTS) is a traditional prescription that has been used for inflammation and bronchial diseases. Coronavirus disease in 2019 (COVID-19), which occurs due to a severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection, is a respiratory inflammatory disease, and mast cells are one of the key cells involved in the cytokine storm. In this study, we aimed to investigate the regulatory effects and mechanisms of BTS and its active compound, α-pinene, on coronavirus infections and inflammatory responses. BTS and α-pinene decreased the expression of not only angiotensin-converting enzyme 2 (ACE2) but also transmembrane protease/serine subfamily member 2 (TMPRSS2) in stimulated human mast cell line, HMC-1 cells. Additionally, BTS and α-pinene significantly suppressed the release of key inflammatory cytokines, including interleukin (IL)-1β, IL-6, IL-8, thymic stromal lymphopoietin, and tumor necrosis factor-α, without compromising cell viability. Furthermore, BTS and α-pinene decreased the expression of transcription factors c-Fos and c-Jun in activated HMC-1 cells. In conclusion, the results of the study indicated that BTS inhibited the c-Jun/c-Fos signaling pathway, leading to a decrease in the levels of ACE2, TMPRSS2, and inflammatory cytokines. This suggests that BTS may be an effective agent in mitigating the cytokine storm induced by SARS-CoV-2 infection.