A notable application of polymeric nanocomposites is the design of water vapor permeable (WVP) membranes. "Breathable" membranes can be created by the incorporation of micro/nanofillers, such as CaCO3, that interrupt the continuity of the polymeric phase and when subjected to additional uniaxial or biaxial stretching this process leads to the formation of micro/nanoporous structures. Among the candidate nanofillers, carbon nanotubes (CNTs) have demonstrated excellent intrinsic WVP properties. In this study, chemically modified MWCNTs with oligo olefin-type groups (MWCNT-g-PP) are incorporated by melt processes into a PP matrix; a β-nucleating agent (β-ΝA) is also added. The crystallization behavior of the nanocomposite films is evaluated by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The WVP performance of the films is assessed via the "wet" cup method. The nanohybrid systems, incorporating both MWCNT-g-PP and β-NA, exhibit enhanced WVP compared to films containing only MWCNT-g-PP or β-NA. This improvement can be attributed to the significant increase in the growth of α-type crystals taking place at the edges of the CNTs. This increased crystal growth exerts a form of stress on the metastable β-phase, thereby expanding the initial microporosity. In parallel, the coexistence of the inherently water vapor-permeable CNTs, further enhances the water vapor permeability reaching a specific water vapor transmission rate (Sp.WVTR) of 5500 μm.g/m2.day in the hybrid composite compared to 1000 μm.g/m2.day in neat PP. Notably, the functionalized MWCNT-g-PP used as nanofiller in the preparation of the "breathable" PP films demonstrated no noteworthy cytotoxicity levels within the low concentration range used, an important factor in terms of sustainability.