Dysbiosis, associated with barrier disruption and altered gut–brain communications, has been associated with multiple sclerosis (MS). In this study, we evaluated the gut microbiota in relapsing–remitting patients (RRMS) receiving disease-modifying therapies (DMTs) and correlated these data with diet, cytokines levels, and zonulin concentrations. Stool samples were used for 16S sequencing and real-time PCR. Serum was used for cytokine determination by flow cytometry, and zonulin quantification by ELISA. Pearson’s chi-square, Mann–Whitney, and Spearman’s correlation were used for statistical analyses. We detected differences in dietary habits, as well as in the gut microbiota in RRMS patients, with predominance of Akkermansia muciniphila and Bacteroides vulgatus and decreased Bifidobacterium. Interleukin-6 concentrations were decreased in treated patients, and we detected an increased intestinal permeability in RRMS patients when compared with controls. We conclude that diet plays an important role in the composition of the gut microbiota, and intestinal dysbiosis, detected in RRMS patients could be involved in increased intestinal permeability and affect the clinical response to DTMs. The future goal is to predict therapeutic responses based on individual microbiome analyses (personalized medicine) and propose dietary interventions and the use of probiotics or other microbiota modulators as adjuvant therapy to enhance the therapeutic efficacy of DMTs.