Novel hybrid polymer inclusion membranes (PIMs) based on poly(vinylidene fluoride) (PVDF) (polymer matrix) and Aliquat 336 (ion carrier) and containing native sodium (Cloisite Na⁺ (CNa)) and organo-modified (Cloisite 30B (C30B)) Montmorillonites were elaborated and tested for the removal of toxic Cr(VI) ions from the aqueous solution. The influence of the nanoclay incorporation on the physicochemical properties of PVDF-based PIMs was studied and the resulting membrane transport properties of the Cr(VI) ions were investigated in detail. The water contact angle measurements reveal that the incorporation of the CNa nanofiller affects the membrane wettability as less hydrophilic surface is obtained in this case—~47° in the presence of CNa as compared with ~15° for PIMs with C30B. The membrane rigidity is found to be dependent on the type and size of the used Montmorillonite. The increase of Young’s modulus is higher when CNa is incorporated in comparison with C30B. The stiffness of the PIM is strongly increased with CNa amount (four times higher with 30 wt %) which is not the case for C30B (only 1.5 times). Higher Cr(VI) permeation flux is obtained for PIMs containing CNa (~2.7 µmol/(m²·s)) owing to their porous structure as compared with membranes loaded with C30B and those without filler (~2 µmol/(m²·s) in both cases). The PIM with 20 wt % of native sodium Montmorillonite revealed satisfactory stability during five cycles of the Cr(VI) transport due to the high membrane rigidity and hydrophobicity. Much lower macromolecular chain mobility in this case allows limiting the carrier loss, thus increasing the membrane stability. On the contrary, a deterioration of the transport performance is recorded for the membrane filled with C30B and that without filler. The obtained results showed the possibility to extend the PIM lifetime through the incorporation of nanoparticles that diminish the carrier loss (Aliquat 336) from the membrane into the aqueous phase by limiting its mobility within the membrane by tortuosity effect and membrane stiffening without losing its permselective properties.