The effect of mechanical milling in i-Al64Cu23Fe13 quasicrystalline and ω-Al70Cu20Fe10 crystalline phases is systematically investigated in the present work. The Al-Cu-Fe samples were obtained by arc furnace technique and then nanostructured by means of mechanical milling. The results indicate that the solid samples present a weak ferromagnetic behavior at 300 K, showing a saturation magnetization of 0.124 emu g-1 for the icosahedral phase (i-phase) and 0.449 emu g-1 for the tetragonal phase (ω-phase). These small values could be an indication that only a few percentage of Fe atoms carry magnetic moment. The magnetic response in the nanostructured ω-phase increases up to 3.5 times higher than its corresponding solid counterpart. Whereas for the i-phase this increment is about 16 times higher. Moreover, the speed of the variation of the studied physical parameters after reducing the average grain size has been obtained from the exponent (α) of a power law fit of the experimental data. The values of α, corresponding to the magnetic response, are slightly different in each phase, which should be related to the different chemical composition and/or the type of long range order. Additionally, we also search for a critical grain size. However, this critical value has not been observed in the studied samples.