Repeated cross-correlations of ambient seismic noise indicate a long-term seismic velocity change associated with the 2006 M7.5 slow-slip event (SSE) in the Guerrero region, Mexico. Because the SSE does not radiate seismic waves, the measured velocity change cannot be associated with the response of superficial soil layers to strong shaking as observed for regular earthquakes. The perturbation observed maximized at periods between 7 s and 17 s, which correspond to surface waves with sensitivity to the upper and middle crust. The amplitude of the relative velocity change (∼10−3) was much larger than the volumetric deformation (∼10−6) at the depths probed (∼5-20 km). Moreover, the time dependence of the velocity perturbation indicated that it was related to the strain rate rather than the strain itself. This suggests that during strong slow-slip events, the deformation of the overlying crust shows significant nonlinear elastic behavior.