Spatially resolved images of the galactic supernova remnant G78.2+2.1 (gamma-Cygni) in hard X-ray energy bands from 25 keV to 120 keV are obtained with the IBIS-ISGRI imager aboard the International Gamma-Ray Astrophysics Laboratory INTEGRAL. The images are dominated by localized clumps of about ten arcmin in size. The flux of the most prominent North-Western (NW) clump is (1.7 +/- 0.4) 10^{-11} erg/cm^2/s in the 25-40 keV band. The observed X-ray fluxes are in agreement with extrapolations of soft X-ray imaging observations of gamma-Cygni by ASCA GIS and spatially unresolved RXTE PCA data. The positions of the hard X-ray clumps correlate with bright patches of optical line emission, possibly indicating the presence of radiative shock waves in a shocked cloud. The observed spatial structure and spectra are consistent with model predictions of hard X-ray emission from nonthermal electrons accelerated by a radiative shock in a supernova interacting with an interstellar cloud, but the powerful stellar wind of the O9V star HD 193322 is a plausible candidate for the NW source as well.