Antiferromagnetic (AFM) spintronics exploits the Néel vector as a state variable for novel electronic devices. Recent studies have demonstrated that the Néel vector can be switched by a spin-orbit torque. These studies however are largely limited to collinear antiferromagnets of proper magnetic space group symmetry. There is, however, a large group of high-temperature noncollinear antiferromagnets, which are suitable for such switching. Here, we predict that spin torque can be efficiently used to switch a noncollinear AFM order in antiperovskite materials. Based on first-principles calculations and atomistic spin-dynamics modeling, we show that in antiperovskites ANMn 3 (A = Ga, Ni, etc.) with the AFM Γ 4g ground state, the AFM order can be switched on the picosecond time scale using a spin torque generated by a spin current. The threshold switching current density can be tuned by the ANMn 3 stoichiometry engineering, changing the magnetocrystalline anisotropy. The Γ 4g AFM phase supports a sizable anomalous Hall effect, which can be used to detect the spin-torque switching of the AFM order. The predicted ultrafast switching dynamics and the efficient detection of the AFM order state make noncollinear magnetic antiperovskites a promising material platform for AFM spintronics.