Attacks by aquatic predators generate frontal water disturbances characterised by low-frequency gradients in pressure and particle motion. Low-frequency hearing is highly developed in cephalopods. Thus, we examined behavioural responses in juvenile cuttlefish to infrasonic accelerations mimicking main aspects of the hydrodynamic signals created by predators. In the experimental set-up, animals and their surrounding water moved as a unit to minimise lateral line activation and to allow examination of the contribution by the inner ear. Behavioural responses were tested in light versus darkness and after food deprivation following a ‘simulated’ hunting opportunity. At low acceleration levels, colour change threshold at 3, 5 and 9 Hz was 0.028, 0.038 and 0.035 m s−2, respectively. At higher stimulus levels, jet-propulsed escape responses thresholds in daylight were 0.043, 0.065 and 0.069 m s−2 at 3, 5 and 9 Hz, respectively, and not significantly different from the corresponding darkness thresholds of 0.043, 0.071 and 0.064 m s−2. In a simulated hunting mode, escape thresholds were significantly higher at 3 Hz (0.118 m s−2) but not at 9 Hz (0.134 m s−2). Escape responses were directional, and overall followed the direction of the initial particle acceleration, with mean escape angles from 313 to 33 deg for all three experiments. Thus, in the wild, particle acceleration might cause escape responses directed away from striking predators but towards suction-feeding predators. We suggest that cuttlefish jet-propulsed escape behaviour has evolved to be elicited by the early hydrodynamic disturbances generated during predator encounters, and that the inner ear plays an essential role in the acoustic escape responses.