This is the first study outside of clinical trials (phase I–III) evaluating the ability of the Ad5-nCoV vaccine to generate neutralizing antibodies and the factors associated with optimal or suboptimal response. In a longitudinal assay, 346 people (117 with prior COVID-19 and 229 without prior COVID-19) vaccinated with Ad5-nCoV were recruited. The percentage of neutralizing antibodies against SARS-CoV-2 (Surrogate Virus Neutralization Test) and antibodies against Ad5 (ADV-Ad5 IgG ELISA) were quantified pre and post-vaccination effects. The Ad5-nCoV vaccine induces higher neutralizing antibodies percentage in individuals with prior COVID-19 than those without prior COVID-19 (median [IQR]: 98% [97–98.1] vs. 72% [54–90], respectively; p < 0.0001). Furthermore, a natural infection (before vaccination) induces more neutralizing antibodies percentage than immunized individuals without prior COVID-19 (p < 0.01). No patient had vaccine-severe adverse effects. The age, antidepressant, and immunosuppressive treatments, reactogenicity, and history of COVID-19 are associated with impaired antibody production. The anti-Ad5 antibodies increased after 21 days of post-vaccination in all groups (p < 0.01). We recommend the application of a booster dose of Ad5-nCoV, especially for those individuals without previous COVID-19 infection. Finally, the induction of anti-Ad5 antibodies after vaccination should be considered if a booster with the same vaccine is planned.