In humans and animals, surprise is a physiological reaction to an unexpected event, but how surprise can be linked to plausible models of neuronal activity is an open problem. We propose a self-supervised spiking neural network model where a surprise signal is extracted from an increase in neural activity after an imbalance of excitation and inhibition. The surprise signal modulates synaptic plasticity via a three-factor learning rule which increases plasticity at moments of surprise. The surprise signal remains small when transitions between sensory events follow a previously learned rule but increases immediately after rule switching. In our model, previously learned rules are protected against overwriting when learning a new rule. Our surprise-modulated spiking network model makes a step towards solving the stability-plasticity dilemma in neuroscience and the problem of continual learning in machine learning.