AI-based autonomous onboard drone applications are evolving rapidly and demand dedicated hardware resources to perform effectively. Currently, CPUs and GPUs are commonly used to run these applications. This paper presents a novel drone platform called MPDrone based on the cutting-edge MPSoC boards that combine FPGA, CPU, and GPU in a single chip. The proposed platform utilizes the reconfigurable FPGA chip to run heavy AI algorithms and the CPU to execute ROS for processing communication with the drone flight controller and onboard sensors. The paper introduces the design and implementation of the MPDrone platform, which is validated in simulation and real-world testing through an intelligent object detection and landing use case. The testing results proved the applicability of the proposed FPGA-based platform for AI applications.