Poly (lactic acid) (PLA)‐based compounds are widely used in thin‐film and food packaging industries. Herein, PLA/ethylene vinyl acetate copolymer (EVA)/nanoclay nanocomposites are prepared in various compositions by melt blending. The gas permeability against N2, CO2, and O2 gases is determined as a function of composition and morphology of the nanocomposites. Inclusion of high aspect ratio of platelet‐like nanoclay to the blend reduces the gas diffusion. The best barrier properties against all gases is observed on introducing 5 wt% poly(ethylene/n‐butyl acrylate glycidyl methacrylate) copolymer as compatibilizer to the PLA/EVA/nanoclay (75/25/5) system. The scanning and transmission electron microscopic analyses and wide‐angle X‐ray scattering studies reveal that inclusion of compatibilizer to the filled‐blends improves the blend morphology, dispersion state, and intercalation level of clay platelets which are preferably localized at the interface of the blend. Analysis of selectivity parameter (α) shows the lowest O2 permeability and the highest αCO2/N2 and αO2/N2 values for the compatibilized filled‐blend (75/25/5/5). In situ aspect ratio of clay and the degree of intercalation are theoretically evaluated based on the permeability data using various empirical models. It is found that the compatibilized filled‐blend has the highest aspect ratio and intercalation level that are responsible for the optimum perm‐selectivity performance.