The magnetically driven metal-insulator transition (MIT) was predicted by Slater in the fifties. Here a long-range antiferromagnetic (AF) order can open up a gap at the Brillouin electronic band boundary regardless of the Coulomb repulsion magnitude. However, while many low-dimensional organic conductors display evidence for an AF driven MIT, in three-dimensional (3D) systems the Slater MIT still remains elusive. We employ terahertz and infrared spectroscopy to investigate the MIT in the NaOsO₃ 3D antiferromagnet. From the optical conductivity analysis we find evidence for a continuous opening of the energy gap, whose temperature dependence can be well described in terms of a second order phase transition. The comparison between the experimental Drude spectral weight and the one calculated through Local Density Approximation (LDA) shows that electronic correlations play a limited role in the MIT. All the experimental evidence demonstrates that NaOsO₃ is the first known 3D Slater insulator.