Driven by the increasing number of connected vehicles and related services, powerful communication and computation capabilities are needed for vehicular communications, especially for real-time and safety-related applications. A cellular network consists of radio access technologies, including the current long-term evolution (LTE), the LTE advanced, and the forthcoming 5th generation mobile communication systems. It covers large areas and has the ability to provide high data rate and low latency communication services to mobile users. It is considered the most promising access technology to support real-time vehicular communications. Meanwhile, fog is an emerging architecture for computing, storage, and networking, in which fog nodes can be deployed at base stations to deliver cloud services close to vehicular users. In fog computing-enabled cellular networks, mobility is one of the most critical challenges for vehicular communications to maintain the service continuity and to satisfy the stringent service requirements, especially when the computing and storage resources are limited at the fog nodes. Service migration, relocating services from one fog server to another in a dynamic manner, has been proposed as an effective solution to the mobility problem. To support service migration, both computation and communication techniques need to be considered. Given the importance of protocol design to support the mobility of the vehicles and maintain high network performance, in this paper, we investigate the service migration in the fog computing-enabled cellular networks. We propose a quality-of-service aware scheme based on the existing handover procedures to support the real-time vehicular services. A case study based on a realistic vehicle mobility pattern for Luxembourg scenario is carried out, where the proposed scheme, as well as the benchmarks, are compared by analyzing latency and reliability as well as migration cost.