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 Ge76 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/c2 to 1 MeV/c2. 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/c2 have been set. As an example, at a mass of 150 keV/c2 the most stringent direct limits on the dimensionless couplings of axionlike particles and dark photons to electrons of gae<3×10-12 and α′/α<6.5×10-24 at 90% credible interval, respectively, were obtained.