This work introduces the one-shot learning paradigm in the computational bioacoustics domain. Even though, most of the related literature assumes availability of data characterizing the entire class dictionary of the problem at hand, that is rarely true as a habitat's species composition is only known up to a certain extent. Thus, the problem needs to be addressed by methodologies able to cope with non-stationarity. To this end, we propose a framework able to detect changes in the class dictionary and incorporate new classes on the fly. We design an one-shot learning architecture composed of a Siamese Neural Network operating in the logMel spectrogram space. We extensively examine the proposed approach on two datasets of various bird species using suitable figures of merit. Interestingly, such a learning scheme exhibits state of the art performance, while taking into account extreme non-stationarity cases.