A two-stage micromechanics technique is used to predict the elastic modulus, as well as the major and minor Poisson’s ratio of unidirectional natural fiber (NF) reinforced composites. The actual NF microstructure consists of cellulose, hemicellulose, lignin, lumen, etc., and these constituents and their contributions are neglected in classical models while quantifying their mechanical properties. The present paper addresses the effect of the real microstructure of the natural jute fiber (JF) by applying a micromechanics approach with the Finite Element Method. Six different hierarchically micro-structured JFs are considered to quantify the JF elastic properties in the first level of homogenization. Later, the JF reinforced polypropylene matrix properties are investigated in the second stage by adopting a homogenization approach. Taking into account the different hierarchical structures (HS), the fiber direction modulus (E1), transverse modulus (E2 and E3), in-plane and out-of-plane shear modulus (G12 and G23), and major (ν12, ν13) and minor (ν23, ν21) Poisson’s ratios are estimated for JF and JF reinforced polypropylene composites. The predicted elastic modulus from micromechanics models is validated against the analytical results and experimental predictions. From the present work, it is observed that the HS of NF needs to be considered while addressing the elastic properties of the NF-reinforced composite for their effective design, particularly at a higher volume fraction of NF.