Cognitive impairment (CI) affects 40–65% of patients with multiple sclerosis (MS). CI can have a negative impact on a patient's everyday activities, such as engaging in conversations. Speech production planning ability is crucial for successful verbal interactions and thus for preserving social and occupational skills. This study investigates the effect of cognitive-linguistic demand and CI on speech production planning in MS, as reflected in speech prosody. A secondary aim is to explore the clinical potential of prosodic features for the prediction of an individual's cognitive status in MS. A total of 45 subjects, that is 22 healthy controls (HC) and 23 patients in early stages of relapsing-remitting MS, underwent neuropsychological tests probing specific cognitive processes involved in speech production planning. All subjects also performed a read speech task, in which they had to read isolated sentences manipulated as for phonological length. Results show that the speech of MS patients with CI is mainly affected at the temporal level (articulation and speech rate, pause duration). Regression analyses further indicate that rate measures are correlated with working memory scores. In addition, linear discriminant analysis shows the ROC AUC of identifying MS patients with CI is 0.70 (95% confidence interval: 0.68–0.73). Our findings indicate that prosodic planning is deficient in patients with MS-CI and that the scope of planning depends on patients’ cognitive abilities. We discuss how speech-based approaches could be used as an ecological method for the assessment and monitoring of CI in MS.