Hidden photons are dark matter candidates motivated by theories beyond the standard model of particle physics. They mix with conventional photons, and they can be detected through the very weak electromagnetic radiation they induce at the interface between a metal and the air. SHUKET (SearcH for U(1) darK matter with an Electromagnetic Telescope) is a dedicated experiment sensitive to the hidden photon-induced signal. The results from a hidden photon search campaign are reported, with no significant detection of a dark matter signal. Exclusion limits are derived from the observed noise fluctuations in a 5 GHz to 6.8 GHz frequency range, corresponding to a hidden photon mass region ranging from 20.8 micro-eV to 28.3 micro-eV. SHUKET is currently the most sensitive instrument in this mass range and the obtained limits on the kinetic mixing term constrain significantly dark matter models inspired from string theory.