The growth of 5G and edge computing has enabled the emergence of Internet of Vehicles. It supports different types of services with different resource and service requirements. However, limited resources at the edge, high mobility of vehicles, increasing demand, and dynamicity in service request-types have made service placement a challenging task. A typical static placement solution is not effective as it does not consider the traffic mobility and service dynamics. Handling dynamics in IoV for service placement is an important and challenging problem which is the primary focus of our work in this paper. We propose a Deep Reinforcement Learning-based Dynamic Service Placement (DRLD-SP) framework with the objective of minimizing the maximum edge resource usage and service delay while considering the vehicle's mobility, varying demand, and dynamics in the requests for different types of services. We use SUMO and MATLAB to carry out simulation experiments. The experimental results show that the proposed DRLD-SP approach is effective and outperforms other static and dynamic placement approaches.