Magnetic Weyl semimetals are an emerging material class that combines magnetic order and a topologically non-trivial band structure. Here, we study ultrafast optically driven spin injection from thin films of the magnetic Weyl semimetals Co2MnGa and Co2MnAl into an adjacent Pt layer by means of terahertz emission spectroscopy. We find that (i) Co2MnGa and Co2MnAl are efficient terahertz spin-current generators reaching efficiencies of typical 3d-transition-metal ferromagnets such as Fe. (ii) The relaxation of the spin current provides an estimate of the electron-spin relaxation time of Co2MnGa (170 fs) and Co2MnAl (100 fs), which is comparable to Fe (90 fs). Both observations are consistent with a simple analytical model and highlight the large potential of magnetic Weyl semimetals as spin-current sources in terahertz spintronic devices. Finally, our results provide a strategy to identify magnetic materials that offer maximum spin-current amplitudes for a given deposited optical energy density.