Heartbeat classification using electrocardiogram (ECG) data is an essential feature of modern day wearable devices. State-of-the-art machine learning-based heartbeat classifiers are designed using convolutional neural networks (CNN). Despite their high classification accuracy, CNNs require significant computational resources and power. This makes the mapping of CNNs on resource-and power-constrained wearable devices challenging. In this paper, we propose heartbeat classification using spiking neural networks (SNN), an alternative approach based on a biologically inspired, event-driven neural networks. SNNs compute and transfer information using discrete spikes that require fewer operations and less complex hardware resources, making them energy-efficient compared to CNNs. However, due to complex error-backpropagation involving spikes, supervised learning of deep SNNs remains challenging. We propose an alternative approach to SNN-based heartbeat classification. We start with an optimized CNN implementation of the heartbeat classification task and then convert the CNN operations, such as multiply-accumulate, pooling and softmax, into spiking equivalent with a minimal loss of accuracy. We evaluate the SNN-based heartbeat classification using publicly available ECG database of the Massachusetts Institute of Technology and Beth Israel Hospital (MIT/BIH), and demonstrate a minimal loss in accuracy when compared to 85.92% accuracy of a CNN-based hearbeat classification. We demonstrate that, for every operation, the activation of SNN neurons in each layer is sparse when compared to CNN neurons, in the same layer. We also show that this sparsity increases with an increase in the number of layers of the neural network. In addition, we detail the power-accuracy trade-off of the SNN and show a 87.76% and 96.82% reduction in SNN neuron and synapse activity,respectively, for accuracy loss ranging between 0.6% and 1.00%, when compared to a CNN-only implementation.