Introduction: Since cognitive impairment (CI) occurs on average in 45% of multiple sclerosis (MS) patients, the early detection of patients “at risk” of CI is important in order to promptly apply preventive strategies. The aim of the present study was to investigate the prevalence and risk factors for CI in MS patients using the Brief International Cognitive Assessment for Multiple Sclerosis (BICAMS) as a screening test. Methods: During the 1-year period, CI was evaluated in 82 consecutives mild relapsing-remitting MS (EDSS ≤ 3.5) patients. Patients with 1 altered BICAMS test were defined “at risk.” Both “at risk” and CI patients underwent an extensive neuropsychological battery. Results: We found that: (i) 23% had CI, (ii), 25% were “at risk” of CI, and (iii) 76% of the “at risk” patients were already impaired at the NP assessment. In particular, the Symbol Digit Modalities Test was the most compromised (70% of “at risk” and 79% of CI patients). Patients with CI had more frequently an EDSS ≥ 2.5 (p = 0.05), lower education (p = 0.05), and relapses in the last 12 months (p = 0.03). Conclusions: CI is a significant issue in MS and integration of a screening test, such as the SDMT, into routine clinical practice could be of worth to identify “at risk” patients and to promote an early therapeutic intervention.