Three monoclonal antibodies—natalizumab (NTZ), ocrelizumab (OCR), and alemtuzumab (ALM)—are the mainstays for the treatment of both relapsing and progressive forms of multiple sclerosis (MS). Here, their safety in patients with MS is analyzed and compared for rational use, especially during the COVID-19 pandemic. All clinical studies published between 2016 and 2020 with the primary outcome of the occurrence of adverse events (AEs) with the use of NTZ, OCR, and ALM in the treatment of MS were systematically searched in the PubMed database. In this review, the percentage of patients reporting AEs was calculated and compared. The most common AEs associated with the use of NTZ, OCR, and ALM were infection and infestation. The percentage of patients reporting urinary tract infection, upper respiratory tract infection, and herpes was 16% using natalizumab, 7% using natalizumab and ocrelizumab, and 2% with ocrelizumab, respectively. The most common AEs, such as rashes, pyrexia, and influenza, were reported with ocrelizumab and alemtuzumab. Additionally, alemtuzumab was associated with immune thrombocytopenia (2%), respiratory infections (7%), and thyroid dysfunction (43%). All these data outcomes show that of the three monoclonal antibodies, natalizumab and ocrelizumab were associated with a reduced incidence of adverse events, making them a safer choice for MS.