A periodically modulated graphene (PMG) generated by nanopatterned surfaces is reported to profoundly modify the intrinsic electronic properties of graphene. The temperature dependence of the sheet resistivity and gate response measurements clearly show a semiconductor-like behavior. Raman spectroscopy reveals significant shifts of the G and the 2D modes induced by the interaction with the underlying grid-like nanostructure. The influence of the periodic, alternating contact with the substrate surface was studied in terms of strain caused by bending of graphene and doping through chemical interactions with underlying substrate atoms. Electronic structure calculations performed on a model of PMG reveals that it is possible to tune a band gap within 0.14-0.19 eV by considering both the periodic mechanical bending and the surface coordination chemistry. Therefore, the PMG can be regarded as a further step toward band gap engineering of graphene devices.