Understanding the relationships between large-scale, low-frequency climate variability modes, fire weather conditions and lighting-ignited wildfires has implications for fire-weather prediction, fire management and conservation. This article proposes a Bayesian network framework for quantifying the influence of climate modes on fire weather conditions and occurrence of lightning-ignited wildfires. The main objectives are to describe and demonstrate a probabilistic framework for identifying and quantifying the joint and individual relationships that comprise the climate-wildfire system; gain insight into potential causal mechanisms and pathways; gauge the influence of climate modes on fire weather and lightning-ignition relative to that of local-scale conditions alone; assess the predictive skill of the network; and motivate the use of techniques that are intuitive, flexible and for which user‐friendly software is freely available. A case study illustrates the application of the framework to a forested region in southwest Australia. Indices for six climate variability modes are considered along with two hazard variables (observed fire weather conditions and prescribed burn area), and a 41-year record of lightning-ignited wildfire counts. Using the case study data set, we demonstrate that the proposed framework: (1) is based on reasonable assumptions provided the joint density of the variables is converted to multivariate normal; (2) generates a parsimonious and interpretable network architecture; (3) identifies known or partially known relationships between the variables; (4) has potential to be used in a predictive setting for fire weather conditions; and (5) climate modes are more directly related to fire weather conditions than to lightning-ignition counts.