Due to the limited computing resources of drones, it is difficult to handle computation-intensive tasks locally, hence, fog-based computation offloading has been widely adopted. The effectiveness of an offloading operation, however, is determined by its ability to infer where the execution of code/data represents less computational effort for the drone, so that, by deciding where to offload correctly, the device benefits. Thus, this paper proposes MonDroneFog, a novel fog-based architecture that supports image offloading, as well as monitoring and storing the performance metrics related to the drone, wireless network, and cloudlet. It takes advantage of the main machine-learning algorithms to provide offloading decisions with high levels of accuracy, F1, and G-mean. We evaluate the main classification algorithms under our database and the results show that Multi-Layer Perceptron (MLP) and Logistic Regression classifiers achieve 99.64% and 99.20% accuracy, respectively. Under these conditions, MonDrone-Fog works well in dense forests when weather conditions are favorable and can be useful as a support system for SAR missions by providing a shorter runtime for image operations.