A growing body of experimental evidence suggests that functional connectivity at rest is shaped by the underlying anatomical structure. Furthermore, the organizational properties of resting-state functional networks are thought to serve as the basis for an optimal cognitive integration. A disconnection at the structural level, as occurring in some brain diseases, would then lead to functional and presumably cognitive impairments. In this work, we propose a computational model to investigate the role of a structural disconnection (encompassing putative local/global and axonal/synaptic mechanisms) on the organizational properties of emergent functional networks. The brain's spontaneous neural activity and the corresponding hemodynamic response were simulated using a large-scale network model, consisting of local neural populations coupled through white matter fibers. For a certain coupling strength, simulations reproduced healthy resting-state functional connectivity with graph properties in the range of the ones reported experimentally. When the structural connectivity is decreased, either globally or locally, the resultant simulated functional connectivity exhibited a network reorganization characterized by an increase in hierarchy, efficiency and robustness, a decrease in small-worldness and clustering and a narrower degree distribution, in the same way as recently reported for schizophrenia patients. Theoretical results indicate that most disconnection-related neuropathologies should induce the same qualitative changes in resting-state brain activity.