The species richness and biodiversity of vegetation in Hungary are increasingly threatened by invasive plant species brought in from other continents and foreign ecosystems. These invasive plant species have spread aggressively in the natural and semi-natural habitats of Europe. Common milkweed (Asclepias syriaca) is one of the species that pose the greatest ecological menace. Therefore, the primary purpose of the present study is to map and monitor the spread of common milkweed, the most common invasive plant species in Europe. Furthermore, the possibilities to detect and validate this special invasive plant by analyzing hyperspectral remote sensing data were investigated. In combination with field reference data, high-resolution hyperspectral aerial images acquired by an unmanned aerial vehicle (UAV) platform in 138 spectral bands in areas infected by common milkweed were examined. Then, support vector machine (SVM) and artificial neural network (ANN) classification algorithms were applied to the highly accurate field reference data. As a result, common milkweed individuals were distinguished in hyperspectral images, achieving an overall accuracy of 92.95% in the case of supervised SVM classification. Using the ANN model, an overall accuracy of 99.61% was achieved. To evaluate the proposed approach, two experimental tests were conducted, and in both cases, we managed to distinguish the individual specimens within the large variety of spreading invasive species in a study area of 2 ha, based on centimeter spatial resolution hyperspectral UAV imagery.