The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has triggered the worldwide coronavirus disease 2019 (COVID-19) pandemic. Serological assays for the detection of SARS-CoV-2 infections are important to understand the immune response in patients and to obtain epidemiological data about the number of infected people, especially to identify asymptomatic persons not aware of a past infection. We recombinantly produced SARS-CoV-2 nucleocapsid (N)-protein in Escherichia coli. We used the purified protein to develop an indirect enzyme-linked immunosorbent assay (ELISA) for the detection of SARS-CoV-2 specific antibodies. This ELISA method was optimized and validated with serum samples collected from 113 patients with RT-PCR-confirmed SARS-CoV-2 infections including hospitalized COVID-19 patients and 1500 control sera mostly collected before 2015 with different clinical background. The optimized N-protein-ELISA provided a sensitivity of 89.7% (n = 68) for samples collected from patients with confirmed SARS-CoV-2 infections and mild to severe symptoms more than 14 days after symptom onset or a positive PCR test. The antibody levels remained low for serum samples collected in the first six days (n = 23) and increased in the second week (n = 22) post symptom onset or PCR confirmation. At this early phase, the ELISA provided a sensitivity of 39.1% and 86.4%, respectively, reflecting the time of an IgG immune response against pathogens. The assay specificity was 99.3% (n = 1500; 95% CI 0.995–0.999). Serum samples from persons with confirmed antibody titers against human immunodeficiency viruses 1/2, parvovirus B19, hepatitis A/B virus, cytomegalovirus, Epstein Barr virus, and herpes simplex virus were tested negative. We conclude that the N-protein-based ELISA developed here is well suited for the sensitive and specific serological detection of SARS-CoV-2 specific IgG antibodies in human serum for symptomatic infections. It may also prove useful to identify previous SARS-CoV-2 infections in vaccinated people, as all currently approved vaccines rely on the SARS-CoV-2 spike (S-) protein.