A theoretical consideration of the so-called "membrane-in-the-middle" optomechanical cavity revealed that it undergoes a spontaneous symmetry breaking as a function of transparency of the membrane. Such typical features of this phenomenon as a square-root development of the order parameter and divergence of the critical susceptibility were identified. In the contrast to a classical spontaneous-symmetry-breaking system of ferroelectrics, in the system considered, this divergence remains, due to interference effects, an "internal" property of the system, which does not reveal itself in any singularity of the output optomechanical response, though the latter is appreciably affected.