Prey fish possess a remarkable ability to sense and evade an attack from a larger fish. Despite the importance of these events to the biology of fishes, it remains unclear how sensory cues stimulate an effective evasive maneuver. Here, we show that larval zebrafish (Danio rerio) evade predators using an escape response that is stimulated by the water flow generated by an approaching predator. Measurements of the high-speed responses of larvae in the dark to a robotic predator suggest that larvae respond to the subtle flows in front of the predator using the lateral line system. This flow, known as the bow wave, was visualized and modeled with computational fluid dynamics. According to the predictions of the model, larvae direct their escape away from the side of their body exposed to more rapid flow. This suggests that prey fish use a flow reflex that enables predator evasion by generating a directed maneuver at high speed. These findings demonstrate a sensory-motor mechanism that underlies a behavior that is crucial to the ecology and evolution of fishes.