(1) Background: The present study aims to report the side effects of vaccination against coronavirus disease 2019 (COVID-19) among patients with multiple sclerosis (MS) who were being treated with disease-modifying therapies (DMTs) in Poland. (2) Methods: The study included 2261 patients with MS who were being treated with DMTs, and who were vaccinated against COVID-19 in 16 Polish MS centers. The data collected were demographic information, specific MS characteristics, current DMTs, type of vaccine, side effects after vaccination, time of side-effect symptom onset and resolution, applied treatment, relapse occurrence, and incidence of COVID-19 after vaccination. The results were presented using maximum likelihood estimates of the odds ratio, t-test, Pearson’s chi-squared test, Fisher’s exact p, and logistic regression. The statistical analyses were performed using STATA 15 software. (3) Of the 2261 sampled patients, 1862 (82.4%) were vaccinated with nucleoside-modified messenger RNA (mRNA) vaccines. Mild symptoms after immunization, often after the first dose, were reported in 70.6% of individuals. Symptoms included arm pain (47.5% after the first dose and 38.7% after the second dose), fever/chills/flu-like symptoms (17.1% after the first dose and 20.5% after the second dose), and fatigue (10.3% after the first dose and 11.3% after the second dose). Only one individual presented with severe side effects (pro-thrombotic complications) after vaccination. None of the DMTs in the presented cohort were predisposed to the development of side effects. Nine patients (0.4%) had a SARS-CoV-2 infection confirmed despite vaccination. (4) Conclusions: Vaccination against SARS-CoV-2 is safe for people with MS who are being treated with DMTs. Most adverse events following vaccination are mild and the acute relapse incidence is low.