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Anti-SARS-CoV-2 spike RBD (receptor-binding domain) IgG antibody levels were monitored in 1643 volunteer healthcare workers of Eginition, Evangelismos, and Konstantopoulio General Hospitals (Athens, Greece), who underwent vaccination with two doses of COVID-19 BNT162b2 mRNA vaccine (Pfizer) and had no history of SARS-CoV-2 infection. Venous blood was collected 20–30 days after the second vaccine dose and anti-RBD IgG levels were determined using CMIA SARS-CoV-2 IgG II Quant (Abbott) on ARCHITECT i System or ADVIA Centaur SARS-CoV-2 IgG (Siemens) on Centaur XP platform. From the total population of 1643 vaccinees (533 M/1110 F; median age = 49; interquartile range-IQR = 40–56), 1636 (99.6%) had anti-SARS-CoV-2 IgG titers above the positivity threshold of the assay used. One-Way ANOVA Kruskal-Wallis H test showed a statistically significant difference in the median of antibody titers between the different age groups (p < 0.0001). Consistently, Spearman’s correlation coefficient (r) for IgGs and age as continuous variables was −0.2380 (p = 1.98 × 10−17). Moreover, antibody titers were slightly higher by 1.2-mean fold (p = 3 × 10−6) in the total female population of the three hospitals (median = 1594; IQR = 875–2584) as compared to males (median = 1292; IQR = 671.9–2188). The present study supports that BNT162b2 vaccine is particularly effective in producing high anti-SARS-CoV-2 IgG levels in healthy individuals, and this humoral response is age- and gender-dependent.