Brain neuronal injury is present in patients suffering from multiple sclerosis (MS) from the earliest stage of the disease; however, the functional counterpart of early neuronal injury is largely unknown. The goal of this study was to assess the potential impact of early neuronal dysfunction affecting white matter (WM), grey matter (GM), or the cerebellum on cognitive deterioration and/or EDSS progression during the first 5 years of MS. Magnetic resonance spectroscopic (MRS) examinations and neuropsychological assessments were performed in 23 patients included after the first clinical attack of MS and 24 healthy controls. The same protocol was performed in patients after a follow-up of 5 years. Metabolic neuronal function was assessed in WM (splenium of corpus callosum), GM (dorsal posterior cingulate cortex), and the cerebellum by evaluating N-acetylaspartate (NAA) levels. During follow-up, 39% of patients showed cognitive deterioration and 43% showed a deterioration in their EDSS. Patients with cognitive deterioration had greater NAA level reductions during follow-up in the cerebellum (p = 0.003) and WM (p = 0.02) compared to patients without cognitive deterioration. In addition, patients with cognitive deterioration had higher progression of T2 lesion load (T2LL) during the follow-up period compared to patients without cognitive deterioration (p = 0.03). No differences between patients with and without EDSS progression in terms of NAA levels or T2LL were observed. The present longitudinal study found evidence that, during the first 5 years of MS, cognitive deterioration is associated with the progression of neuronal dysfunction and tissue injury as assessed by MRS and T2LL, respectively.