Aquaponics is an emerging area of agricultural sciences that combines aquaculture and hydroponics in a symbiotic way to enhance crop production. A stable smart aquaponic system requires estimating the fish size in real time. Though deep learning has shown promise in the context of smart aquaponics, most smart systems are extremely slow and costly and cannot be deployed on a large scale. Therefore, we design and present a novel neuromorphic computer that uses spiking neural networks (SNNs) for estimating not only the length but also the weight of the fish. To train the SNN, we present a novel hybrid scheme in which some of the neural layers are trained using direct SNN backpropagation, while others are trained using standard backpropagation. By doing this, a blend of high hardware efficiency and accuracy can be achieved. The proposed computer SpikoPoniC can classify more than 84 million fish samples in a second, achieving a speedup of at least 3369× over traditional general-purpose computers. The SpikoPoniC consumes less than 1100 slice registers on Virtex 6 and is much cheaper than most SNN-based hardware systems. To the best of our knowledge, this is the first SNN-based neuromorphic system that performs smart real-time aquaponic monitoring.