  We show that optomechanical systems can test the Schr\"{o}dinger-Newton
equation of gravitational quantum mechanics due to Yang et al. This equation is
motivated by semiclassical gravity, a widely used theory of interacting
gravitational and quantum fields. From the many-body Schr\"{o}dinger-Newton
equation follows an approximate equation for the center-of-mass dynamics of
macroscopic objects. This predicts a distinctive double-peaked signature in the
output optical quadrature power spectral density of certain optomechanical
systems. Since the Schr\"{o}dinger-Newton equation lacks free parameters, these
will allow its experimental confirmation or refutation.
