We report on efficient electronic energy transfer from excitons confined in silicon (Si) nanocrystals to molecular oxygen (MO). The remarkable photosensitizing properties of Si nanocrystal assemblies result from a broad energy spectrum of photoexcited excitons, a long triplet exciton lifetime and a highly developed surface area. Quenching of photoluminescence (PL) of Si nanocrystals by MO physisorbed on their surface is found to be most efficient when the energy of excitons coincides with the triplet-singlet splitting energy of oxygen molecules. Spectroscopic analysis of the quenched PL spectrum evidences that energy transfer is accompanied by multi-phonon emission. From time-resolved measurements the characteristic time of energy transfer is found to be in the range of microseconds. The dependence of PL quenching efficiency on the surface termination of nanocrystals is consistent with short-range resonant electron exchange mechanism of energy transfer. The energy transfer to oxygen molecules in the gaseous phase at elevated temperatures is demonstrated.