The photo-oxidative studies of ethylene vinyl acetate copolymer (EVA) matrix, filled with Layered Double Hydroxide (LDH) modified with methacrylic anion (MA), were herein reported, together with gas permeation tests. The formulation of nano-hybrid LDHs was characterized using X-ray diffractometry (XRD) and thermogravimetric analysis (TGA), demonstrating the partial intercalation of the 30% of MA anion between the LDH’s galleries. The as-modified filler was introduced into an EVA matrix by mechanical milling, producing free-standing films subjected to accelerated aging. Fourier transform infrared spectroscopy (FT-IR) results suggested that the nanohybrid presence determined a stabilizing effect up to 45 days of UV irradiation, especially if compared to the EVA/LDH references for all formulated EVA hybrid nanocomposites. Conversely, the presence of nanohybrid in the matrix did not significantly change the thermal stability of EVA samples. The dispersion of modified MA-LDH in the EVA matrix produces defect-free samples in the whole range of investigated loadings. The samples show a slight decrease in gas permeability, coupled with a substantial stabilization of the original CO2/O2 selectivity, which also proves the integrity of the films after 30 days of UV irradiation.