Very weakly coupled new-physics particles in the MeV-GeV range appear as mediators in various "portals" to a hidden sector. Their interaction with Standard Model particles is feeble and these states are usually long-lived, so that the experimental search fully profits of a high-intensity setup, such as that of fixed-target experiments. Within the vector portal hidden-sector model a dark photon might exist which predominantly decays to dark matter particles. A search for such an invisible particle has been performed, exploiting the efficient photon-veto capability and high resolution tracking of the NA62 detector at CERN. The signal stems from the chain K+ → π+π0 followed by the π0 decay to a photon-dark-photon pair. No significant statistical excess has been identified. Upper limits on the dark photon coupling to the ordinary photon as a function of the dark photon mass have been set.