For 5G wireless communication networks, low latency and high spectral efficiency are required to provide ubiquitous communication for emerging applications. In this letter, we propose a novel framework which considers these requirements simultaneously by integrating the notion of effective capacity (EC) and non-orthogonal multiple access (NOMA) into virtualized wireless networks (VWNs). At first, we consider a virtual base station architecture to achieve isolation between different service providers (slices). Then, a resource allocation design for maximization of the EC is formulated as a non-convex optimization problem which takes into account the average maximum power constraints and delay quality-of-service requirements. To strike a balance between computational complexity and system performance, we apply the successive convex approximation to the non-convex optimization problem. Subsequently, an iterative low-complexity suboptimal algorithm is proposed. Numerical results illustrate that there is a non-trivial fundamental tradeoff between delay and spectral efficiency in VWNs while NOMA provides a significant improvement in terms of EC compared to conventional orthogonal multiple access.