Recently, Fifth Generation (5G) cellular networks have gained promise as a paradigm that could provide rich computational resources for users. Virtualization is a key technology for wireless communications, especially in standard Long Term Evolution (LTE) systems, which enable cloud based multi-tenancy business models through providing a shared scalable resource platform for all users. Despite the potential significance of virtualization for cellular networks, several challenges remain to be addressed. For cellular networks, providing multiple levels of security is essential to support different levels in information sensitivity. However, placing different customers' services requirements on a virtualized evolved Node B's (eNB's) scheduler may lead to noticeable security vulnerabilities. In this work, we present an overview of cellular network security issues in a fully virtualized environment along with their preventative measures. Virtualization is implemented by allowing service providers to share their resources while performing different scheduling policies and sharing one eNB. To evaluate the considered framework, the average delays for different traffic types were measured. The results of the simulation showed that virtualization could noticeably reduce average user equipment delay compared with the non-sharing scheme.