SARS-CoV-2 is currently causing a devastating pandemic and there is a pressing need to understand the dynamics, specificity, and neutralizing potency of the humoral immune response during acute infection. Herein, we report the dynamics of antibody responses to the receptor-binding domain (RBD) of the spike protein and virus neutralization activity in 44 COVID-19 patients. RBD-specific IgG responses were detectable in all patients 6 days after PCR confirmation. Using a clinical isolate of SARS-CoV-2, neutralizing antibody titers were also detectable in all patients 6 days after PCR confirmation. The magnitude of RBD-specific IgG binding titers correlated strongly with viral neutralization. In a clinical setting, the initial analysis of the dynamics of RBD-specific IgG titers was corroborated in a larger cohort of PCR-confirmed patients (n=231). These findings have important implications for our understanding of protective immunity against SARS-CoV-2, the use of immune plasma as a therapy, and the development of much-needed vaccines.