We describe a magnetic relation in analogy to the well-known dielectric Lyddane-Sachs-Teller relation [R. H. Lyddane et al., Phys. Rev. 59, 673 (1941)]. This magnetic relation follows directly from the model equations for nuclear induction due to fast oscillating electromagnetic fields [F. Bloch, Phys. Rev. 70, 460 (1946)] and relates the static permeability with the product over all ratios of antiresonance and resonance frequencies associated with all magnetic excitations within a given specimen. The magnetic relation differs significantly from its dielectric analog where the static properties are related to ratios of the squares of resonance frequencies. We demonstrate the validity of the magnetic Lyddane-Sachs-Teller relation using optical magnetization data from terahertz electron magnetic resonance spectroscopic ellipsometry measurements in the presence of an external magnetic field on an iron-doped semiconductor crystal of gallium nitride.