We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.