The groundbreaking discoveries of gravitational waves from binary black-hole mergers and, most recently, coalescing neutron stars started a new era of Multi-Messenger Astrophysics and revolutionized our understanding of the Cosmos. Machine learning techniques such as artificial neural networks are already transforming many technological fields and have also proven successful in gravitational-wave astrophysics for detection and characterization of gravitational-wave signals from binary black holes. Here we use a deep-learning approach to rapidly identify transient gravitational-wave signals from binary neutron star mergers in noisy time series representative of typical gravitational-wave detector data. Specifically, we show that a deep convolution neural network trained on 100,000 data samples can rapidly identify binary neutron star gravitational-wave signals and distinguish them from noise and signals from merging black hole binaries. These results demonstrate the potential of artificial neural networks for real-time detection of gravitational-wave signals from binary neutron star mergers, which is critical for a prompt follow-up and detailed observation of the electromagnetic and astro-particle counterparts accompanying these important transients.