Recent studies have demonstrated disrupted topological organization of brain connectome in multiple sclerosis (MS). However, whether the communication efficiency between different functional systems is affected in the early stage of MS remained largely unknown. In this study, we constructed the structural connectivity (SC) and functional connectivity (FC) networks in 41 patients with clinically isolated syndrome (CIS), 32 MS patients and 35 healthy controls (HC) based on diffusion and resting-state functional MRI. To quantify the communication efficiency within and between different functional systems, we proposed two measures called intra- and inter-module efficiency. Based on the module parcellation of functional backbone network, the intra- and inter-module efficiency of SC and FC networks was calculated for each participant. For the SC network, CIS showed decreased inter-module efficiency between the sensory-motor network (SMN), the visual network (VN), the default-mode network (DMN) and the fronto-parietal network (FPN) compared with HC, while MS showed more widespread decreased module efficiency both within and between modules relative to HC and CIS. For the FC network, no differences were found between CIS and HC, and a decreased inter-module efficiency between SMN and FPN and between VN and FPN was identified in MS, compared with HC and CIS. Moreover, both intra- and inter-module efficiency of SC network were correlated with the disability and cognitive scores in MS. Therefore, our results demonstrated early SC changes between modules in CIS, and more widespread SC alterations and inter-module FC changes were observed in MS, which were further associated with cognitive impairment and physical disability.