Infection with severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), the cause of coronavirus disease 2019 (COVID-19), is initiated by the interaction between a receptor protein, angiotensin-converting enzyme type 2 (ACE2) on the cell surface, and the viral spike (S) protein. This interaction is similar to the mechanism in SARS-CoV, a close relative of SARS-CoV-2, which was identified in 2003. Drugs and antibodies that inhibit the interaction between ACE2 and S proteins could be key therapeutic methods for preventing viral infection and replication in COVID-19. Here, we demonstrate the interaction between human ACE2 and a fragment of the S protein (S1 subunit) derived from SARS-CoV-2 and SARS-CoV using two-color fluorescence cross-correlation spectroscopy (FCCS), which can detect the interaction of fluorescently labeled proteins. The S1 subunit of SARS-CoV-2 interacted in solution with soluble ACE2, which lacks a transmembrane region, more strongly than that of SARS-CoV. Furthermore, one-to-one stoichiometry of the two proteins during the interaction was indicated. Thus, we propose that this FCCS-based interaction detection system can be used to analyze the interaction strengths of various mutants of the S1 subunit that have evolved during the worldwide pandemic, and also offers the opportunity to screen and evaluate the performance of drugs and antibodies that inhibit the interaction.