The ground-state properties of the half-filled Hubbard model are investigated in the framework of lattice density functional theory. The single-particle density matrix γijσ is regarded as the central variable of the many-body problem, where i and j refer to the lattice sites and σ to the spin. The interaction-energy functional W[γijσ] is calculated exactly for representative finite periodic systems by performing exact Lanczos diagonalizations. The relationship between W[γijσ] and the entropy S[ηkσ] of independent fermions with natural-orbital occupations ηkσ is analyzed. A simple approximation to the interaction energy of the half-filled Hubbard model is proposed, which takes the form W=W(S[ηkσ]). Using this functional we derive the ground-state energy, kinetic energy, average number of double occupations, charge distribution, magnetic susceptibility, and field-induced spin polarization in one-, two-, and three-dimensional periodic lattices. The limit of infinite dimensions is also explored. The accuracy of the method is assessed by comparison with available exact numerical or analytical results. Goals, limitations, and possible extensions of the domain of applicability of the functional are discussed.