We propose a micromechanical model for the behavior of dilute magnetorheological fluids under unidirectional slow-compression, constant-volume squeeze flow mode. In the linear magnetization regime, the model predicts a power law scaling of the normal stress with the particle volume fraction and magnetic field strength squared at low fields. The predictions are satisfactorily compared with experimental measurements for different particle loadings, sample volume, surface roughness, and initial gap distance.