By leveraging the elasticity of cloud computing, cloud radio access network (C-RAN) facilitates on-demand radio and computing resource provisioning. In this paper, we propose an energy-efficient on-demand C-RAN virtualization model which dynamically provisions virtual C-RAN according to service demand. The energy consumption of the virtual C-RAN is minimized by jointly optimizing the remote radio head (RRH) selection and computing resource provisioning. The network energy consumption minimization problem is challenging because of the interdependence between the RRH selection and the computing resource provisioning. We propose the energy-efficient on-demand C-RAN virtualization (REACT) algorithm to solve the problem in two steps. First, we cluster RRHs into groups using the hierarchical clustering analysis (HCA) algorithm and assign a BBU to each RRH group for the baseband signal processing. Second, we determine the RRH selection by optimizing the cooperative beamforming. The performance of the proposed algorithm is evaluated through extensive simulations, which shows the proposed algorithm reduces up to 62% of the network energy consumption as compared to a baseline algorithm.