Characterization of multivariate time series of behaviour data from animal-borne sensors is challenging. Biologists require methods to objectively quantify baseline behaviour, then assess behaviour changes in response to environmental stimuli. Here, we apply hidden Markov models (HMMs) to characterize blue whale movement and diving behaviour, identifying latent states corresponding to three main underlying behaviour states: shallow feeding, travelling, and deep feeding. The model formulation accounts for inter-whale differences via a computationally efficient discrete random effect, and measures potential effects of experimental acoustic disturbance on between-state transition probabilities. We identify clear differences in blue whale disturbance response depending on the behavioural context during exposure, with whales less likely to initiate deep foraging behaviour during exposure. Findings are consistent with earlier studies using smaller samples, but the HMM approach provides more nuanced characterization of behaviour changes.