Network function virtualization (NFV) allows software-oriented network functions executed on general-purpose servers or virtual machines (VMs) instead of dedicated hardware, greatly improving the flexibility and scalability of network services. Consequently, NFV would facilitate versatile and dynamic network measurement services to meet the increasingly diversified measurement demands. However, it is challenging to provision the measurement services in a virtualized environment due to the stochastic nature in measurement demand and the special requirements of measurement functions such as location constraint and execution time. In this paper, we compose a measurement service chain as a Virtual Measurement Function (VMF) graph, and then propose a dynamic VMF scheduling algorithm for a software-oriented measurement system using Lyapunov optimization technique to maximize the revenue of the system while guaranteeing the Quality of Service (QoS). The scheduling algorithm decides whether to accept a measurement service request and which measurement nodes (MNs) instantiate the VMF graph. Finally, the performance of our proposed algorithm is verified through theoretical analysis and numerical evaluation. The simulation results show that the proposed algorithm can increase the total avenue by up to 10%, reduce the service average queue delay by 24%, and decrease the service reject rate by up to 10%, comparing with a heuristic algorithm.