Recent experiments on van der Waals antiferromagnets have shown that measuring the temperature ( T ) and magnetic field ( H ) dependence of the conductance allows their magnetic phase diagram to be mapped. Similarly, experiments on ferromagnetic CrBr ₃ barriers enabled the Curie temperature to be determined at H  = 0, but a precise interpretation of the magnetoconductance data at H  ≠ 0 is conceptually more complex, because at finite H there is no well-defined phase boundary. Here we perform systematic transport measurements on CrBr ₃ barriers and show that the tunneling magnetoconductance depends on H and T exclusively through the magnetization M ( H ,  T ) over the entire temperature range investigated. The phenomenon is reproduced by the spin-dependent Fowler–Nordheim model for tunneling, and is a direct manifestation of the spin splitting of the CrBr ₃ conduction band. Our analysis unveils a new approach to probe quantitatively different properties of atomically thin ferromagnetic insulators related to their magnetization by performing simple conductance measurements.