Photonic crystal membranes (PCM) provide a versatile planar platform for on-chip implementations of photonic quantum circuits. One prominent quantum element is a coupled system consisting of a nanocavity and a single quantum dot (QD) which forms a fundamental building block for elaborate quantum information networks and a cavity quantum electrodynamic (cQED) system controlled by single photons. So far no fast tuning mechanism is available to achieve control within the system coherence time. Here we demonstrate dynamic tuning by monochromatic coherent acoustic phonons formed by a surface acoustic wave (SAW) with frequencies exceeding 1.7 gigahertz, one order of magnitude faster than alternative approaches. We resolve a periodic modulation of the optical mode exceeding eight times its linewidth, preserving both the spatial mode profile and a high quality factor. Since PCMs confine photonic and phononic excitations, coupling optical to acoustic frequencies, our technique opens ways towards coherent acoustic control of optomechanical crystals.