While cognitive abilities in people with multiple sclerosis (PwMS) have been studied in detail, little is known about linguistic abilities in PwMS and their relation to cognitive impairment. In this cross-sectional explorative study, we aim to investigate the morphosyntactic abilities of PwMS alongside their cognitive performance. Furthermore, we explore the effect of clinical factors, namely, the disease duration and MS type, on the linguistic and cognitive performance of PwMS. By so doing, we aim to shed light on neurocognitive and clinical correlates of linguistic performance in PwMS. We included 78 patients and 78 age-, sex- and education-matched healthy individuals. All participants were additionally administered the Brief International Cognitive Assessment for Multiple Sclerosis (BICAMS) battery, a verbal short-term memory task (non-word repetition) and questionnaires about mood, fatigue and quality of life. In addition, they underwent examinations with morphology and syntax tasks. PwMS were found to be impaired in morphology (past tense) and selectively impaired in syntax alongside cognitive impairments. Disease duration had the main impact on cognitive abilities. The MS type selectively impacted linguistic abilities, as shown by the remarkably deficient performance of the MS individuals with the progressive disease subtype. Linguistic impairments were predicted by only one measure of the BICAM test, namely, the Symbol Digit Modalities Test (SDMT), a measure of cognitive processing speed. Overall, this study contributes to the better understanding of the linguistic profile of PwMS by reporting selective deficits in their morphological and syntactical abilities. Furthermore, it provides insights into the clinical and cognitive correlates of linguistic performance. By so doing, it suggests clinical implications for the development of intervention programs for PwMS.