The control of acoustic phonons, which are the carriers of sound and heat, has become the focus of increasing attention because of a demand for manipulating the sonic and thermal properties of nanometric devices. In particular, the photoacoustic effect using ultrafast optical pulses has a promising potential for the optical manipulation of phonons in the picosecond time regime. So far, its mechanism has been mostly based on the commonplace thermoelastic expansion in isotropic media, which has limited applicability. In this study, we investigate a conceptually new mechanism of the photoacoustic effect involving a structural instability that utilizes a transition-metal dichalcogenide VTe2 with a ribbon-type charge-density-wave (CDW). Ultrafast electron microscope imaging and diffraction measurements reveal the generation and propagation of unusual acoustic waves in a nanometric thin plate associated with optically induced instantaneous CDW dissolution. Our results highlight the capability of photoinduced structural instabilities as a source of coherent acoustic waves.