Brain connectivity, allowing information to be shared between distinct cortical areas and thus to be processed in an integrated way, has long been considered critical for consciousness. However, the relationship between functional intercortical interactions and the structural connections thought to underlie them is poorly understood. In the present work, we explore both functional (with an EEG-based metric: the median weighted symbolic mutual information in the theta band) and structural (with a brain MRI-based metric: fractional anisotropy) connectivities in a cohort of 78 patients affected with a disorder of consciousness. Both metrics could distinguish patients in a vegetative state from patients in minimally conscious state. Crucially, we discovered a significant positive correlation between functional and structural connectivities. Furthermore, we showed that this structure-function relationship is more specifically observed when considering structural connectivity within the intra-and interhemispheric long-distance cortico-cortical bundles involved in the Global Neuronal Workspace (GNW) theory of consciousness, thus supporting predictions of this model. Altogether, these results support the interest of multimodal assessments of brain connectivity in refining the diagnostic evaluation of patients with disorders of consciousness.