Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with the increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized correlation-induced quiver motion of the electrons. The finite-lattice enhancement dominates the HHG spectra from a few harmonic orders until a threshold from which the correlational enhancement dominates. This threshold is determined by the degree of correlation and decreases into the low-frequency regime for increasing electron-electron correlation. This infers that as the electron-electron correlation increases, the finite-size effect on the electron dynamics decreases.