Ecosystems driven by wildfire regimes are characterized by fire size distributions resembling power laws. Existing models produce power laws, but their predicted exponents are too high and fail to capture the exponent’s variation with geographic region. Here we present a minimal model of fire dynamics that describes fire spread as a stochastic birth-death process, analogous to stochastic population growth or disease spread and incorporating memory effects from previous fires. The model reproduces multiple regional patterns in fire regimes and allows us to classify different regions in terms of their proximity to a critical threshold. Transitions across this critical threshold imply abrupt and pronounced increases in average fire size. The model predicts that large regions in Canada are currently close to this transition and might be driven beyond the threshold in the future. We illustrate this point by analyzing the time series for large fires (>199 ha) from the Canadian Boreal Plains, found to have shifted from a subcritical regime to a critical regime in the recent past. By contrast to its predecessor, the model also suggests that a critical transition, and not self-organized criticality, underlies forest fire dynamics, with implications for other ecological systems exhibiting power-law-like patterns, in particular for their sensitivity to environmental change and control efforts.