We present an evaluation of different deep learning and machine learning approaches for tree health classification in the Black Forest, the Harz Mountains, and the Göttinger Forest on a unique, highly accurate tree-level dataset. The multispectral UAV data were collected from eight forest plots with diverse tree species, mostly conifers. As ground truth data (GTD), nearly 1500 tree polygons with related attribute information on the health status of the trees were used. This data were collected during extensive fieldwork using a mobile application and subsequent individual tree segmentation. Extensive preprocessing included normalization, NDVI calculations, data augmentation to deal with the underrepresented classes, and splitting the data into training, validation, and test sets. We conducted several experiments using a classical machine learning approach (random forests), as well as different convolutional neural networks (CNNs)—ResNet50, ResNet101, VGG16, and Inception-v3—on different datasets and classes to evaluate the potential of these algorithms for tree health classification. Our first experiment was a binary classifier of healthy and damaged trees, which did not consider the degree of damage or tree species. The best results of a 0.99 test accuracy and an F1 score of 0.99 were obtained with ResNet50 on four band composites using the red, green, blue, and infrared bands (RGBI images), while VGG16 had the worst performance, with an F1 score of only 0.78. In a second experiment, we also distinguished between coniferous and deciduous trees. The F1 scores ranged from 0.62 to 0.99, with the highest results obtained using ResNet101 on derived vegetation indices using the red edge band of the camera (NDVIre images). Finally, in a third experiment, we aimed at evaluating the degree of damage: healthy, slightly damaged, and medium or heavily damaged trees. Again, ResNet101 had the best performance, this time on RGBI images with a test accuracy of 0.98 and an average F1 score of 0.97. These results highlight the potential of CNNs to handle high-resolution multispectral UAV data for the early detection of damaged trees when good training data are available.