Granular systems, without any energy injection, tend to be clustered or condensed due to inelasticity of the particle collisions. Even in a driven granular gas, this notable phenomenon would be present locally and lead to a spatial inhomogeneity, just like the forming of liquid droplets in gases. The present work, by extending an existing two-dimensional theory, offers a three-dimensional model for such a phase-separation phenomenon in a driven granular gas under zero gravity. According to the model, exact conditions for phase separation are obtained through numerical calculations. Event-driven molecular dynamics simulations confirm the theoretical results, and show new morphologies of phase separation in three-dimensional granular gases.