According to theoretical views, the non-dissipative Josephson current through nano-scale junctions is carried by spectroscopically sharp energy states, so-called Andreev bound states. We have proposed a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single- level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy ωA≈2EA, and a superconducting-phase dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift is proposed for the Andreev bound state spectroscopy. Future work will study non-equilibrium conditions where the resonator circuit is driven by an external field.