Deficits in rhythm perception and production have been reported in a variety of psychiatric, neurodevelopmental and neurologic disorders. Since correlations between rhythmic abilities and cognitive functions have been demonstrated in neurotypical individuals, we here investigate whether and how rhythmic abilities are associated with cognitive functions in 35 participants with neurocognitive deficits due to acquired brain lesions. We systematically assessed a diverse set of rhythm perception and production abilities including time and beat perception and finger-tapping tasks. Neuropsychological tests were applied to assess separable cognitive functions. Using multiple regression analyses we show that lower variability in aligning movements to a pacing sequence was predicted by better inhibitory control and better working memory performance. Working memory performance also predicted lower variability of rhythmic movements in the absence of an external pacing sequence and better anticipatory timing to sequences with gradual tempo changes. Importantly, these predictors remained significant for all regression models when controlling for other cognitive variables (i.e., cognitive flexibility, information processing speed, and verbal learning ability) and potential confounders (i.e., age, symptom strength of depression, manual dexterity, duration of illness, severity of cognitive impairment, and musical experience). Thus, all rhythm production abilities were significantly predicted by measures of executive functions. In contrast, rhythm perception abilities (time perception/beat perception) were not predicted by executive functions in this study. Our results, enhancing the understanding of cognitive underpinnings of rhythmic abilities in individuals with neurocognitive deficits, may be a first mandatory step to further potential therapeutic implications of rhythm-based interventions in neuropsychological rehabilitation.