We propose a way to include magnetic dipole-dipole interactions in density functional theory calculations. To this end, we derive an approximation to the exchange-correlation energy functional associated with the spin-spin correction to the Coulomb force in the Breit-Pauli Hamiltonian. The local spin-density approximation is shown to be identically zero. First order nonlocal corrections are evaluated analytically within linear response to a noncollinear external magnetic field. The functional obtained is based on the exact-exchange energy of the magnetic electron gas with dipolar interactions and is estimated to be relevant at interatomic distances, or in the low electron density limit, where it amounts to one quarter of the magnetostatic energy. We expect our functional to improve over the current description of ground-state properties of inhomogeneous magnetic structures at the nanoscale and dipolar spin systems.