A droplet bouncing on a vibrated bath becomes a "walker" moving at constant velocity on the interface when it couples to the surface wave it generates. Here the motion of a walker is investigated when it collides with barriers of various thicknesses. Surprisingly, it undergoes a form of tunneling: the reflection or transmission of a given incident walker is unpredictable. However, the crossing probability decreases exponentially with increasing barrier width. This shows that this wave-particle association has a nonlocality sufficient to generate a quantumlike tunneling at a macroscopic scale.