Magnetically-induced birefringence is usually low in molecular liquids owing to the low magnetic energy of molecules with respect to the thermal one. Despite this, it has been found that a mixture of dibutyl phosphate and propylamine at propylamine molar ratio (X) around 0.33 surprisingly gives an intense effect (∆n/λ ≈ −0.1 at 1 Tesla). In this paper the time- and intensity- response to the magnetic field of such mixture have been studied. It was found that the reaction to the magnetic field is unusually slow (from several minutes to hours) depending of the magnetic field intensity. On the basis of the data, the model of orientable dipoles dispersed in a matrix enables to interpret the magnetic field-induced self-assembly in terms of soft molecules-based nanostructures. The analogy with systems made of magnetically polarizable (solid or soft) particles dispersed in liquid carrier allows understanding, at the microscopic scale, the molecular origin and the supra-molecular dynamics involved in the observed behavior. The data present a novel phenomenon in liquid phase where the progressive building up/change of ordered and strongly interacting amphiphiles is driven by the magnetic field.