Ultrafast laser texturing allows the reliable generation of surface micro- and nano-structures on steel substrates. Laser-induced textures show a wide range of structure geometries, from the micro to the nano-scale. The replication of submicron surface structures by micro injection molding is a crucial factor in achieving advanced functionalities, such as antimicrobial resistance, in mass-produced plastic products. In this work, we investigate and model the replication quality of laser-induced periodic surface structures by micro injection molding of different bio-based polymers. A comprehensive multiscale model was developed to predict the submicron scale polymer flow, using a numerical model to analyze the polymer behavior in the mold macro cavity and determine the boundary conditions for the filling of the surface structures. The replication of the mold topography was modeled considering topographical parameters, polymer rheology and thermal behavior, and the mold surface energy, which was modified by depositing an atomic layer of alumina on the steel surface structures. The modeling approach was validated against injection molding experiments, in which the mold temperature was varied due to its well-known influence on replication. The sensitivity to polymer selection, mold surface properties, and mold temperature, was captured. A maximum error of 8% showed the accuracy of the multi-scale model.