Patients with multiple sclerosis (MS) often experience cognitive impairment, and this is related to structural disconnection and subsequent functional reorganization. It is unclear how specific patterns of functional reorganization might make it harder for cognitively impaired (CI) patients with MS to dynamically adapt how brain regions communicate, which is crucial for normal cognition. We aimed to identify dynamic functional network patterns that are relevant to cognitive impairment in MS and investigate whether these patterns can be explained by altered energy costs. Resting-state functional and diffusion MRI was acquired in a cross-sectional design, as part of the Amsterdam MS cohort. Patients with clinically definitive MS (relapse-free) were classified as CI (≥2/7 domains Z < -2), mildly CI (MCI) (≥2/7 domains Z < -1.5), or cognitively preserved (CP) based on an expanded Brief Repeatable Battery of Neuropsychological Tests. Functional connectivity states were determined using k-means clustering of moment-to-moment cofluctuations (i.e., edge time series), and the resulting state sequence was used to characterize the frequency of transitions. Control energy of the state transitions was calculated using the structural network with network control theory. Imaging and cognitive data were available for 95 controls and 330 patients (disease duration: 15 years; 179 CP, 65 MCI, and 86 CI). We identified a "visual network state," "sensorimotor network state," "ventral attention network state," and "default mode network state." CI patients transitioned less frequently between connectivity states compared with CP (β = -5.78; p = 0.038). Relative to the time spent in a state, CI patients transitioned less from a "default mode network state" to a "visual network state" (β = -0.02; p = 0.004). The CI patients required more control energy to transition between states (β = 0.32; p = 0.007), particularly for the same transition (β = 0.34; p = 0.049). This study showed that it costs more energy for MS patients with cognitive impairment to dynamically change the functional network, possibly explaining why these transitions occur less frequently. In particular, transitions from a default mode network state to a visual network state were relevant for cognition in these patients. To further study the order of events leading to these network disturbances, future work should include longitudinal data across different disease stages.