In this study we have investigated the interaction of phenylalanine (Phe), histidine (His), tyrosine (Tyr), and tryptophan (Tryp) molecules with graphene and single walled carbon nanotubes (CNTs) with an aim to understand the effect of curvature on the non-covalent interaction. The calculations are performed using density functional theory and the Møller-Plesset second-order perturbation theory (MP2) within linear combination of atomic orbitals-molecular orbital (LCAO-MO) approach. Using these methods, the equilibrium configurations of these complexes were found to be very similar, i.e., the aromatic rings of the amino acids prefer to orient in parallel with respect to the plane of the substrates, which bears the signature of weak π -π interactions. The binding strength follows the trend: His<Phe<Tyr<Tryp. Although the qualitative trend in binding energy is almost similar between the planar graphene and rolled nanotube structure but they differ in terms of the absolute magnitude. For the nanotube, the binding strength of these molecules is found to be weaker than the graphene sheet. To get an insight about the nature of these interactions, we have calculated the polarizability of the aromatic motifs of the amino acids. Remarkably, we find excellent correlation between the polarizability and the strength of the interaction; the higher the polarizability, greater is the binding strength. Moreover, we have analyzed the electronic densities of state spectrum before and after adsorption of the amino acid moieties. The results reveal that the Fermi level of the free CNT is red-shifted by the adsorption of the amino acids and the degree of shift is consistent with the trend in polarizability of these molecules.