Cognitive impairment and deficits in social cognition (SC) are frequent in patients with multiple sclerosis (MS). The aim of the present work is to study SC in patients with early MS and to analyze its neuroanatomical correlation. Thirty-four patients with relapsing remitting MS, with ≤ 2 years of disease progression and EDSS and ≤2, and 30 healthy control subjects matched for age, sex, and educational level were recruited. Subjects performed a comprehensive neuropsychological assessment (Rao BRB). SC was assessed using the International Affective Picture System IAPS, The Eyes in the Mind Test, the Empathy Quotient, and the Faux Pas Test. The anatomical correlation of patients with deficits in social cognition was studied through brain MRI and voxel-based morphometric for which cortical reconstruction and volumetric segmentation were performed using Freesurfer processing software. Patients showed significant deficits in executive functions, verbal memory and language tests. SC assessment showed that patients presented greater difficulties in the Faux Pas Test (p = 0.023), The Mind in the Eyes Test (p = 0.014), and presented a positive bias in the interpretation of neutral images of the IAPS (P = 0.023). Furthermore, patients with CS deficits presented less cortical thickness in areas of the right supramarginal gyrus, pars opercularis, and anterior cingulum.