The Internet of Things (IoT), which consists of a large number of small low-cost devices, has become a leading solution for smart cities, smart agriculture, smart buildings, smart grids, e-healthcare, etc. Integrating unmanned aerial vehicles (UAVs) with IoT can result in an airborne UAV-based IoT (UIoT) system and facilitate various value-added services from sky to ground. In addition to wireless sensors, various kinds of IoT devices are connected in UIoT, making the network more heterogeneous. In a UIoT system, for achieving high throughput in an energy-efficient manner, it is crucial to design an efficient medium access control (MAC) protocol because the MAC layer is responsible for coordinating access among the IoT devices in the shared wireless medium. Thus, various MAC protocols with different objectives have been reported for UIoT. However, to the best of the authors’ knowledge, no survey had been performed so far that dedicatedly covers MAC protocols for UIoT. Hence, in this study, state-of-the-art MAC protocols for UIoT are investigated. First, the communication architecture and important design considerations of MAC protocols for UIoT are examined. Subsequently, different MAC protocols for UIoT are classified, reviewed, and discussed with regard to the main ideas, innovative features, advantages, limitations, application domains, and potential future improvements. The reviewed MAC protocols are qualitatively compared with regard to various operational characteristics and system parameters. Additionally, important open research issues and challenges with recommended solutions are summarized and discussed.