We measure the quantum fluctuations of a single acoustic mode in a volume of superfluid He that is coupled to an optical cavity. Specifically, we monitor the Stokes and anti-Stokes light scattered by a standing acoustic wave that is confined by the cavity mirrors. The intensity of these signals (and their cross-correlation) exhibits the characteristic features of the acoustic wave's zero-point motion and the quantum backaction of the intracavity light. While these features are also observed in the vibrations of solid objects and ultracold atomic gases, their observation in superfluid He opens the possibility of exploiting the remarkable properties of this material to access new regimes of quantum optomechanics.