Cognitive dysfunction affects 40-65% of multiple sclerosis (MS) patients and can occur in the early stages of the disease. This study aimed to explore cognitive functions by means of the Italian version of the minimal assessment of cognitive function in MS (MACFIMS) in relapsing-remitting MS (RRMS) patients with very mild clinical disability to identify the primarily involved cognitive functions. Ninety-two consecutive RRMS patients with Expanded Disability Status Scale (EDSS) scores ≤ 2.5 and forty-two healthy controls (HC) were investigated. Our results show that 51.1% of MS patients have cognitive dysfunction compared to HC. An impairment of verbal and visual memory, working memory, and executive functions was found in the RRMS group. After subgrouping RRMS by EDSS, group 1 (EDSS ≤ 1.5) showed involvement of verbal memory and executive functions; moreover, group 2 (2 ≤ EDSS ≤ 2.5) patients were also impaired in information processing speed and visual memory. Our results show that utilizing a comprehensive neuropsychological assessment, approximately half of MS patients with very mild physical disability exhibit cognitive impairment with a primary involvement of prefrontal cognitive functions. Detecting impairment of executive functions at an early clinical stage of disease could be useful to promptly enroll MS patients in targeted rehabilitation.