This paper presents an evaluation of different convolutional neural network (CNN) architectures using false-colour images obtained by multispectral sensors on drones for the detection of Black Sigatoka in banana crops. The objective is to use drones to improve the accuracy and efficiency of Black Sigatoka detection to reduce its impact on banana production and improve the sustainable management of banana crops, one of the most produced, traded, and important fruits for food security consumed worldwide. This study aims to improve the precision and accuracy in analysing the images and detecting the presence of the disease using deep learning algorithms. Moreover, we are using drones, multispectral images, and different CNNs, supported by transfer learning, to enhance and scale up the current approach using RGB images obtained by conventional cameras and even smartphone cameras, available in open datasets. The innovation of this study, compared to existing technologies for disease detection in crops, lies in the advantages offered by using drones for image acquisition of crops, in this case, constructing and testing our own datasets, which allows us to save time and resources in the identification of crop diseases in a highly scalable manner. The CNNs used are a type of artificial neural network widely utilised for machine training; they contain several specialised layers interconnected with each other in which the initial layers can detect lines and curves, and gradually become specialised until reaching deeper layers that recognise complex shapes. We use multispectral sensors to create false-colour images around the red colour spectra to distinguish infected leaves. Relevant results of this study include the construction of a dataset with 505 original drone images. By subdividing and converting them into false-colour images using the UAV’s multispectral sensors, we obtained 2706 objects of diseased leaves, 3102 objects of healthy leaves, and an additional 1192 objects of non-leaves to train classification algorithms. Additionally, 3640 labels of Black Sigatoka were generated by phytopathology experts, ideal for training algorithms to detect this disease in banana crops. In classification, we achieved a performance of 86.5% using false-colour images with red, red edge, and near-infrared composition through MobileNetV2 for three classes (healthy leaves, diseased leaves, and non-leaf extras). We obtained better results in identifying Black Sigatoka disease in banana crops using the classification approach with MobileNetV2 as well as our own datasets.