The literature suggests that real-world data on the effectiveness and safety of the BNT162b2 vaccine depend on the characteristics of the vaccinated volunteers. The purpose of this study was to evaluate antibody responses and kinetics, established association with sociodemographic and clinical characteristics, and adverse reactions after complete vaccination with the BNT162b2 vaccine. A single-center prospective case series study was conducted with 112 eligible volunteers who were institutionalized elderly and health care workers with had a negative anti-SARS-CoV-2 IgG test prior to receiving the first dose of vaccine. At least one serological antibody test after each dose of vaccine was performed. Volunteers with a positive SARS-CoV-2 PCR test before vaccination were excluded. A chemiluminescent immunoassay anti-S1 antibody assay performed a serological evaluation. Both vaccine doses elicited positive IgG antibodies 3799.0 ± 2503.0 AU/mL and 8212.0 ± 4731.0 AU/mL after 20 days of the first and second doses of BNT162b2, respectively. Comirnaty® vaccine induced an immune response with antibody production against SARS-CoV-2 in 100% of participants, regardless of age (Spearman rho = −0.10, p-value = 0.312), body mass index (Spearman rho = 0.05, p-value = 0.640), blood group first dose (p-value for Kruskal–Wallis test = 0.093) and second dose (p-value for Kruskal–Wallis test = 0. 268), number of drugs (Spearman rho = −0.07, p-value = 0.490), and number of chronic diseases first dose (p-value for Kruskal–Wallis test = 0.632) and second dose (p-value for Kruskal–Wallis test = 0.510). IgG antibodies to SARS-CoV-2 were intensely elevated after the second administration of the BNT162b2 vaccine. The higher the titer of anti-peptide IgG antibodies generated after the first dose of vaccine, the higher the titer generated by the second dose of vaccine (Spearman rho = 0.86, p-value < 0.001) and the total antibody titer (Spearman rho = 0.93, p-value < 0.001). Furthermore, no serious adverse effects were reported among participants, although mild to moderate adverse effects (local or systemic) were reported after both doses of the BNT162b2 vaccine, being more frequent after the first dose of the vaccine. No participants showed a positive PCR. The BNT162b2 vaccine induces a robust and rapid antibody response regardless of participant characteristics. The second dose might be especially important because of the increased immunogenicity it produces and the possible temporal distancing of the interval between doses. In general, the vaccines were well tolerated.