The proliferation of novel infotainment services, such as virtual reality (VR)-based services, has fundamentally changed the existing mobile networks. These bandwidth-hungry services expanded at a tremendously rapid pace, thus, generating a burden of data traffic in the mobile networks. To cope with this issue, one can use multiaccess edge computing (MEC) to bring the resource to the edge. By doing so, we can release the burden of the core network by taking the communication, computation, and caching resources nearby the end users (UEs). Nevertheless, due to the vast adoption of VR-enabled devices, MEC resources might be insufficient in peak times or dense settings. To overcome these challenges, we propose a system model where the service provider (SP) might rent unmanned area vehicles (UAVs) from UAV SPs (USPs) to serve as micro-base stations (UBSs) that expand the service area and improve the spectrum efficiency. In which, UAV can precached certain sets of VR-based contents and serve UEs via air-to-ground (A2G) communication. Furthermore, future intelligent devices are capable of 5G and B5G communication interfaces, and thus, they can communicate with UAVs via A2G links. By doing so, we can significantly reduce a considerable amount of data traffic in mobile networks. In order to successfully enable such kinds of services, an attractive incentive mechanism is required. Therefore, we propose a contract theory-based incentive mechanism for UAV-assisted MEC in VR-based infotainment services, in which the MEC offers an amount reward to a UAV for serving as a UBS in a specific location for certain time slots. We then derive an optimal contract-based scheme with individual rationality and incentive compatibility conditions. The numerical findings show that our proposed approach outperforms the linear pricing (LP) technique and is close to the optimal solution in terms of social welfare. Additionally, our proposed scheme significantly enhanced the fairness of utility for UAVs in asymmetric information problems.