Network function virtualization (NFV) is considered to be a promising paradigm for reducing network infrastructure cost. However, the mapping from network physical resources to service function chain (SFC), which is an ordered sequence of virtual network functions, is challenging, especially when a dynamic wireless network is involved. In this article, we propose a novel lightweight SFC embedding framework based on reinforcement learning in the NFV-enabled wireless network for reducing the end-to-end wired and wireless delay and leveraging the SFC acceptance ratio. We model the embedding problem as a Markov decision process, in which the reward is modeled as an adjustable weighted function, including combined delay (wired and wireless delay) and remaining resource. Accordingly, a lightweight and adjustable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -learning-based SFC embedding strategy is proposed. To validate the effectiveness of our proposed framework, extensive simulations are performed by using real data traces and compared with a classical genetic algorithm (GA) and a cluster-based method MAPLE. The results of the simulation show that the proposed framework is efficient and performs better than both GA and MAPLE in terms of delay and service acceptance probability. The prototype of the framework is also built for demonstrating the feasibility of the proposed framework.