We present the first search for bosonic superweakly interacting massive particles (super-WIMPs) as keV-scale dark matter candidates performed with the GERDA experiment. GERDA is a neutrinoless double-β decay experiment which operates high-purity germanium detectors enriched in ^{76}Ge in an ultralow background environment at the Laboratori Nazionali del Gran Sasso (LNGS) of INFN in Italy. Searches were performed for pseudoscalar and vector particles in the mass region from 60 keV/c^{2} to 1 MeV/c^{2}. No evidence for a dark matter signal was observed, and the most stringent constraints on the couplings of super-WIMPs with masses above 120 keV/c^{2} have been set. As an example, at a mass of 150 keV/c^{2} the most stringent direct limits on the dimensionless couplings of axionlike particles and dark photons to electrons of g_{ae}<3×10^{-12} and α^{'}/α<6.5×10^{-24} at 90% credible interval, respectively, were obtained.