We report on optical experiments performed on individual GaAs nanowires and the manipulation of their temporal emission characteristics using a surface acoustic wave. We find a pronounced, characteristic suppression of the emission intensity for the surface acoustic wave propagation aligned with the axis of the nanowire. Furthermore, we demonstrate that this quenching is dynamical as it shows a pronounced modulation as the local phase of the surface acoustic wave is tuned. These effects are strongly reduced for a SAW applied in the direction perpendicular to the axis of the nanowire due to their inherent one-dimensional geometry. We