With the development of drone technology, concerns have arisen about the possibility of drones being equipped with threat payloads for terrorism and other crimes. A drone detection system that can detect drones carrying payloads is needed. A drone’s propeller rotation frequency increases with payload weight. Therefore, a method for estimating propeller rotation frequency will effectively detect the presence or absence of a payload and its weight. In this paper, we propose a method for classifying the payload weight of a drone by estimating its propeller rotation frequency from radar images obtained using a millimeter-wave fast-chirp-modulation multiple-input and multiple-output (MIMO) radar. For each drone model, the proposed method requires a pre-prepared reference dataset that establishes the relationships between the payload weight and propeller rotation frequency. Two experimental measurement cases were conducted to investigate the effectiveness of our proposal. In case 1, we assessed four drones (DJI Matrice 600, DJI Phantom 3, DJI Mavic Pro, and DJI Mavic Mini) to determine whether the propeller rotation frequency of any drone could be correctly estimated. In case 2, experiments were conducted on a hovering Phantom 3 drone with several payloads in a stable position for calculating the accuracy of the payload weight classification. The experimental results indicated that the proposed method could estimate the propeller rotation frequency of any drone and classify payloads in a 250 g step with high accuracy.