While many patients infected by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) eventually produce neutralising antibodies, the degree of susceptibility of previously infected individuals to reinfection by SARS-CoV-2 is currently unknown. To better understand the impact of the immunoglobulin (IgG) level on reinfection in recovered coronavirus disease 2019 (COVID-19) patients, anti-nucleocapsid IgG levels against SARS-CoV-2 were measured in 829 patients with previously confirmed infection just after their recovery. Notably, 87 of these patients had no detectable IgG concentration. While there was just one case of asymptomatic reinfection 4.5 months after the initial recovery amongst patients with detectable anti-nucleocapsid IgG levels, 25 of the 87 patients negative for anti-nucleocapsid IgG were reinfected within one to three months after their first infection. Therefore, patients who recover from COVID-19 with no detectable anti-nucleocapsid IgG concentration appear to remain more susceptible to reinfection by SARS-CoV-2, with no apparent immunity. Also, although our results suggest the chance is lower, the possibility for recovered patients with positive anti-nucleocapsid IgG findings to be reinfected similarly exists.