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This paper presents a novel ECG classification algorithm for inclusion as part of real-time cardiac monitoring systems in ultra low-power wearable devices. The proposed solution is based on spiking neural networks which are the third generation of neural networks. In specific, we employ spike-timing dependent plasticity (STDP), and reward-modulated STDP (R-STDP), in which the model weights are trained according to the timings of spike signals, and reward or punishment signals. Experiments show that the proposed solution is suitable for real-time operation, achieves comparable accuracy with respect to previous methods, and more importantly, its energy consumption in real-time classification of ECG signals is significantly smaller. In specific, energy consumption is 1.78 μJ per beat, which is 2 to 9 orders of magnitude smaller than previous neural network based ECG classification methods.