Heteroepitaxial n-ZnO films have been grown on commercial p-type 6H-SiC substrates by plasma-assisted molecular-beam epitaxy, and n-ZnO/p-SiC heterojunction mesa structures have been fabricated and their photoresponse properties have been studied. Current-voltage characteristics of the structures had a very good rectifying diode-like behavior with a leakage current less than 2 x 10-4 A/cm2 at -10 V, a breakdown voltage greater than 20 V, a forward turn on voltage of ∼5 V, and a forward current of ∼2 A/cm2 at 8 V. Photosensitivity of the diodes, when illuminated from ZnO side, was studied at room temperature and photoresponsivity of as high as 0.045 A/W at -7.5 V reverse bias was observed for photon energies higher than 3.0 eV.