The production of $K^{0}_{S}$ mesons in inelastic p+p collisions at beam momentum 158 $\text{ GeV }/c$ ($\sqrt{s_{NN}}=17.3$ $\text{ GeV }$) was measured with the NA61/SHINE spectrometer at the CERN Super Proton Synchrotron. Double-differential distributions were obtained in transverse momentum and rapidity. The mean multiplicity of $K^{0}_{S}$ was determined to be $0.162 \pm 0.001 (stat.) \pm 0.011 (sys.)$. The results on $K^{0}_{S}$ production are compared with model predictions (EPOS 1.99, SMASH 2.0, PHSD and UrQMD 3.4 models) as well as with published world data.