Herein we report the fabrication of molecular nanostructures on surfaces via two-dimensional (2D) folding of the nine amino acid peptide bradykinin. Soft-landing electrospray ion beam deposition in conjunction with high-resolution imaging by scanning tunneling microscopy is used to fabricate and investigate the molecular nanostructures. Subnanometer resolved images evidence the large conformational freedom of the molecules if thermal motion is inhibited and the formation of stable uniform dimers of only one specific conformation when diffusion can take place. Molecular dynamics modeling supported by density functional theory calculations give atomically precise insight into the induced-fit binding scheme when the folded dimer is formed. In the absence of solvent, we find a hierarchy of binding strength from polar to nonpolar, manifested in an inverted polar nonpolar segregation which suppresses unspecific interactions at the rim of the nanostructure. The demonstrated 2D-folding scheme resembles many key properties of its native 3D counterpart and shows that functional, molecular nanostructures on surfaces fabricated by folding could be just as versatile and specific.