We report a measurement of the ionization efficiency of silicon nuclei recoiling with sub-keV kinetic energy in the bulk silicon of a charge-coupled device (CCD). Nuclear recoils are produced by low-energy neutrons (<24  keV) from a Sb124−Be9 photoneutron source, and their ionization signal is measured down to 60 eV electron equivalent. This energy range, previously unexplored, is relevant for the detection of low-mass dark matter particles. The measured efficiency is found to deviate from the extrapolation to low energies of the Lindhard model. This measurement also demonstrates the sensitivity to nuclear recoils of CCDs employed by DAMIC, a dark matter direct detection experiment located in the SNOLAB underground laboratory.