Massive photon-like particles are predicted in many extensions of the Standard Model with a hidden sector where dark matter is secluded. Most of the present experimental constraints on this "dark photon" ($A'$) rely on the hypothesis of dominant decay to lepton pairs.
The PADME experiment at Laboratori Nazionali di Frascati of INFN, by annihilating the positrons of the DA$\Phi$NE Beam-Test Facility on a carbon target, will search for the e$^+$e$^- \rightarrow \gamma$A$^{\prime}$ process, assuming a decay of the $A'$ into invisible particles of the hidden sector. A fine-grained, high-resolution calorimeter will measure the momentum of the photon in events with no other signal in the apparatus, thus allowing to identify the $A'$ as a missing mass in the final state.
In about one year of data taking, a sensitivity on the interaction strength ($\varepsilon$) down to 0.001 is achievable in the mass region M(A$^{\prime}$) $<$ 23.7 MeV$/c^2$.
The status of PADME and its physics potential are here reviewed.