This study characterizes antibody and T-cell immune responses over time until the booster dose of COronaVIrus Disease 2019 (COVID-19) vaccines in patients with multiple sclerosis (PwMS) undergoing different disease-modifying treatments (DMTs). We prospectively enrolled 134 PwMS and 99 health care workers (HCWs) having completed the two-dose schedule of a COVID-19 mRNA vaccine within the last 2–4 weeks (T0) and followed them 24 weeks after the first dose (T1) and 4–6 weeks after the booster (T2). PwMS presented a significant reduction in the seroconversion rate and anti-receptor-binding domain (RBD)-Immunoglobulin (IgG) titers from T0 to T1 (p < 0.0001) and a significant increase from T1 to T2 (p < 0.0001). The booster dose in PwMS showed a good improvement in the serologic response, even greater than HCWs, as it promoted a significant five-fold increase of anti-RBD-IgG titers compared with T0 (p < 0.0001). Similarly, the T-cell response showed a significant 1.5- and 3.8-fold increase in PwMS at T2 compared with T0 (p = 0.013) and T1 (p < 0.0001), respectively, without significant modulation in the number of responders. Regardless of the time elapsed since vaccination, most ocrelizumab- (77.3%) and fingolimod-treated patients (93.3%) showed only a T-cell-specific or humoral-specific response, respectively. The booster dose reinforces humoral- and cell-mediated-specific immune responses and highlights specific DMT-induced immune frailties, suggesting the need for specifically tailored strategies for immune-compromised patients to provide primary prophylaxis, early SARS-CoV-2 detection and the timely management of COVID-19 antiviral treatments.