A new ternary Ir-Mn-Si phase with stoichiometry Mn3IrSi has been synthesized and found to crystallize in the cubic AlAu4-type structure, space group P213 with Z=4, which is an ordered form of the beta-Mn structure. The unit cell dimension was determined by x-ray powder diffraction to a=6.4973(3) Angstrom. In addition to the crystal structure, we have determined the magnetic structure and properties using superconducting quantum interference device magnetometry and Rietveld refinements of neutron powder diffraction data. A complex noncollinear magnetic structure is found, with magnetic moments of 2.97(4)u(B) at 10 K only on the Mn atoms. The crystal structure consists of a triangular network built up by Mn atoms, on which the moments are rotated 120degrees around the triangle axes. The magnetic unit cell is the same as the crystallographic and carries no net magnetic moment. The Neel temperature was determined to be 210 K. A first-principles study, based on density functional theory in a general noncollinear formulation, reproduces the experimental results with good agreement. The observed magnetic structure is argued to be the result of frustration of antiferromagnetic couplings by the triangular geometry.