The application of deep learning techniques may prove difficult when datasets are small. Recently, techniques such as one-shot learning, few-shot learning, and Siamese networks have been proposed to address this problem. In this paper, we propose the use a convolutional Siamese network (CSN) that learns a similarity metric that discriminates between plant species based on images of leaves. Once the CSN has learned the similarity function, its discriminatory power is generalized to classify not just new pictures of the species used during training but also entirely new species for which only a few images are available. This is achieved by exposing the network to pairs of similar and dissimilar observations and minimizing the Euclidean distance between similar pairs while simultaneously maximizing it between dissimilar pairs. We conducted experiments to study two different scenarios. In the first one, the CSN was trained and validated with datasets that comprise 5, 10, 15, 20, 25, and 30 pictures per species, extracted from the well-known FLAVIAmathsizesmall dataset. Then, the trained model was tested with another dataset composed of 320 images (10 images per species) also from FLAVIAmathsizesmall. The obtained accuracy was compared with the results of feeding the same training, validation, and testing datasets to a convolutional neural network (CNN) in order to determine if there is a threshold value for dataset size that defines the intervals for which either the CSN or the CNN has better accuracy. In the second studied scenario, the accuracy of both the CSN and the CNN-both trained and validated with the same datasets extracted from FLAVIAmathsizesmall-were compared when tested on a set of images of leaves of 20 Costa Rican tree species that are not represented in FLAVIAmathsizesmall.