Based on density-functional calculations, we propose that ZrMn₂ is a polymorphic material. We predict that at low temperatures the cubic C15, and the hexagonal C14 and C36 structures of the Laves phase compound ZrMn₂ are nearly equally stable within 0.3 kJ mol⁻¹ or 30 K. This degeneracy occurs when the Mn atoms magnetize spontaneously in a ferromagnetic arrangement forming the states of lowest energy. From the temperature-dependent free energies at T ≈ 160 K we predict a transition from the most stable C15 to the C14 structure, which is the experimentally observed structure at elevated temperatures.