Autonomous vehicles interacting with other traffic participants heavily rely on the perception and prediction of other agents’ behaviors to plan safe trajectories. However, as occlusions limit the vehicle’s perception ability, reasoning about potential hazards beyond the field of view is one of the most challenging issues in developing autonomous driving systems. This paper introduces a novel analytical approach that poses safe trajectory planning under occlusions as a hybrid zero-sum dynamic game between the autonomous vehicle (evader) and an initially hidden traffic participant (pursuer). Due to occlusions, the pursuer’s state is initially unknown to the evader and may later be discovered by the vehicle’s sensors. The analysis yields optimal strategies for both players as well as the set of initial conditions from which the autonomous vehicle is guaranteed to avoid collisions. We leverage this theoretical result to develop a novel trajectory planning framework for autonomous driving that provides worst-case safety guarantees while minimizing conservativeness by accounting for the vehicle’s ability to actively avoid other road users as soon as they are detected in future observations. Our framework is agnostic to the driving environment and suitable for various motion planners. We demonstrate our algorithm on challenging urban and highway driving scenarios using the open-source CARLA simulator.