Cognitive dysfunction is well known in patients suffering from multiple sclerosis (MS) and has been described for many years. Cognitive impairment, memory, and attention deficits seem to be features of advanced MS stages, whereas depression and emotional instability already occur in early stages of the disease. However, little is known about processing of affective prosody in patients in early stages of relapsing–remitting MS (RRMS). In this study, tests assessing attention, memory, and processing of affective prosody were administered to 25 adult patients with a diagnosis of RRMS at an early stage and to 25 healthy controls (HC). Early stages of the disease were defined as being diagnosed with RRMS in the last 2 years and having an Expanded Disability Status Scale (EDSS) of 2 or lower. Patients and HC were comparable in intelligence quotient (IQ), educational level, age, handedness, and gender. Patients with early stages of RRMS performed below the control group with respect to the subtests ‘discrimination of affective prosody’ and ‘matching of affective prosody to facial expression’ for the emotion ‘angry’ of the ‘Tübingen Affect Battery’. These deficits were not related to executive performance. Our findings suggest that emotional prosody comprehension is deficient in young patients with early stages of RRMS. Deficits in discriminating affective prosody early in the disease may make misunderstandings and poor communication more likely. This might negatively influence interpersonal relationships and quality of life in patients with RRMS.