Sleep disorders are common in people with multiple sclerosis (PwMS) and could contribute to cognitive dysfunction. However, effects of pathological sleep on cognitive domains are insufficiently characterized. To evaluate associations between cognitive performance and polysomnographic (PSG)-based sleep disturbances in PwMS. PwMS with known/suspected untreated obstructive sleep apnea (OSA, N = 131) underwent PSG and cognitive tests: Symbol Digit Modalities Test (SDMT), Paced Auditory Serial Addition Test (PASAT), California Verbal Learning Test-II (CVLT-II), Brief Visuospatial Memory Test-Revised (BVMT-R Total and Delayed), Judgment of Line Orientation (JLO), Controlled Oral Word Association Test (COWAT), Trail Making Test, Go/No-Go, and Nine-Hole Peg Test (NHPT). Apnea severity measures were associated with worse processing speed, attention, and working memory (SDMT); immediate and delayed visual memory (BVMT-R Total and Delayed); attention, psychomotor speed, and cognitive flexibility (Trails); and manual dexterity and visuomotor coordination (NHPT) (ps ⩽ 0.011). Sleep macrostructure measures showed stronger associations with verbal memory and response inhibition (CVLT-II Total Recognition Discriminability Index), and immediate visual memory (BVMT-R Total) (ps ⩽ 0.011). Pathological sleep, including hypoxia, sleep fragmentation, and disturbances in sleep/wake states, are differentially associated with worse cognitive performance in PwMS. These findings could inform future personalized approaches to cognitive impairment in PwMS with sleep disorders. ClinicalTrials.gov identifier: NCT02544373 (https://clinicaltrials.gov/ct2/show/NCT02544373).