Background: The COVID-19 pandemic posed significant challenges for people with multiple sclerosis (PwMS) in Oman, including heightened stress, treatment disruptions, and risks associated with immunosuppressive therapies. This study aimed to evaluate the pandemic’s impact on MS management, COVID-19 incidence and outcomes, psychosocial and mental health effects, and demographic and clinical predictors influencing these outcomes among Omani PwMS. Methods: In this cross-sectional study conducted from January to April 2021, 104 PwMS aged 18–60 participated in structured interviews and completed the Expanded Disability Status Scale (EDSS) and the World Health Organization Well-being Index (WHO-5). Clinical data on relapse rates, disease-modifying therapies (DMTs), and treatment adherence were analyzed using descriptive and inferential statistics. Results: Of the participants, 76 (73.1%) were female, and 23 (22.1%) reported contracting COVID-19, with fatigue being the most common symptom (87%). Female sex (p = 0.042), younger age (18–34 vs. 35–45 years; p = 0.014), COVID-19 diagnosis (p = 0.037), and lower mental well-being scores (p = 0.021) were strongly associated with COVID-19-related effects. Conclusions: Key predictors of self-reported COVID-19 effects in Omani PwMS were a confirmed diagnosis, female sex, younger age, and lower mental well-being. These findings highlight the need for exploration of mental resilience in this group and interventions during crises.