Multiple Sclerosis (MS) is the most common chronic autoimmune disease of the central nervous system, affecting around 2.8 million people worldwide. Patients’ knowledge about COVID-19 infection, and their proper protective actions, may reduce the risk of infection. The aim of this study was to assess the knowledge of patients with MS about SARS-CoV-2, COVID-19 illness, the relationship between MS and COVID-19, willingness to be vaccinated, and the impact of the pandemic on MS care. An original, anonymous, 35-items, self-reported questionnaire was used in both web-based and on-site survey formats. Two-hundred and forty-eight questionnaires were analyzed (mean age 40.8 ± 10.6 years, 77.8% women). Participants reported the use of multiple sources of information, and the most common were websites (77.8%) and television (59.3%). The majority of participants knew the correct symptoms of COVID-19 or transmission routes (94.4%), and accepted the pandemic’s restrictions (96.8%). A total of 93.2% considered SARS-CoV-2 as highly infectious, and 69% thought they were at higher risk of being infected with SARS-CoV-2, mainly because of immunodeficiency (82.7%). Although most of them were afraid of COVID-19 (69.0%), only two-thirds wanted to be vaccinated. Patients who were afraid of COVID-19 had a 3.5-times higher chance to declare willingness for vaccination. A total of 29.8% patients claimed that the COVID-19 pandemic limited access to the healthcare system. This study shows that Polish patients with MS represent a good level of knowledge about COVID-19 disease, and acceptance for public rules, but their willingness for vaccinations is not sufficient. Country-wide educational campaigns should be conducted, particularly on the internet and TV. Restrictions in healthcare facilities should be balanced to secure access for patients with MS.