We study the nearest-neighbor Heisenberg antiferromagnet on a face-centered cubic lattice with arbitrary spin S. The model exhibits degenerate classical ground states including two collinear structures AF1 and AF3 described by different propagation vectors that are prime candidates for the quantum ground state. We compute the energy for each of the two states as a function of S using the spin-wave theory that includes magnon-magnon interaction in a self-consistent way and the numerical coupled cluster method. Our results unambiguously demonstrate that quantum fluctuations stabilize the AF1 state for realistic values of spin. Transition to the harmonic spin-wave result, which predicts the AF3 state, takes place only for S > 10. We also study quantum renormalization of the magnon spectra for both states as a function of spin.