We investigated the variation of the electronic band gap of ZnO bulk and that of bent ZnO nanowires under the influence of uniaxial strain by using density functional theory. By applying a strain of about ± to bulk ZnO in equilibrium, we mimic the recent experimentally determined tensile and compressive strain along the c axis of ZnO microwires which results from the bending of such wires. The slope of band gap size versus tensile-compressive strain at the equilibrium gives a deformation potential parameter, the value of which ranges between -2.0 and -4.0 eV depending on the exchange correlation treatments applied in order to improve the absolute value of the band gap. We find that the local (local density approximation) and semilocal [generalized gradient approximation (GGA) and the meta-GGA] approximations to the exchange-correlation functionals give a deformation potential, which is in good agreement with experiments. It is shown that the elastic constants derived from bulk ZnO are sufficient to model the strain effects for microwires. On the other hand, nanowires, only a few Å in diameter, respond with stronger changes in the band gap to applied strain. This feature, however, approaches the bulk behavior as the thickness of the nanowire increases.