Double-differential yields of $\Xi\left(1530\right)^{0}$ and $\overline{\Xi}\left(1530\right)^{0}$ resonances produced in \pp interactions were measured at a laboratory beam momentum of 158~\GeVc. This measurement is the first of its kind in \pp interactions below LHC energies. It was performed at the CERN SPS by the \NASixtyOne collaboration. Double-differential distributions in rapidity and transverse momentum were obtained from a sample of 26$\cdot$10$^6$ inelastic events. The spectra are extrapolated to full phase space resulting in mean multiplicity of $\Xi\left(1530\right)^{0}$ (6.73 $\pm$ 0.25 $\pm$ 0.67)$\times10^{-4}$ and $\overline{\Xi}\left(1530\right)^{0}$ (2.71 $\pm$ 0.18 $\pm$ 0.18)$\times10^{-4}$. The rapidity and transverse momentum spectra and mean multiplicities were compared to predictions of string-hadronic and statistical model calculations.