Zirconium oxide (ZrO₂) is a wide and direct band gap semiconductor having potential to be used in making fuel cells, protective coatings for mirrors and optoelectronic devices. The optoelectronic devices fabricated on ZrO₂ span wide optical range depending on the band gap of ZrO₂ material. The band gap of ZrO₂ can be tuned by fabricating it to nanoscale. In this paper, we synthesized the ZrO₂ nanostructures on quartz substrate using ZrO₂ ions produced by the ablation of ZrO₂ pellet due to high temperature, high density and extremely non-equilibrium argon plasma in a modified dense plasma focus device. Uniformly distributed monoclinic ZrO₂ nanostructures of average dimension ~ 14 nm have been obtained as found from X-ray diffraction and Scanning electron microscopy studies. The monoclinic phase of ZrO₂ nanostructures is further confirmed from photoluminescence (PL) and Raman spectra. PL spectra show peaks in ultra-violet (UV) and near-UV regions with tunable band gap of nanostructures. Similar tunability of band gap has been observed from absorption spectra. The obtained structural, morphological and optical properties are correlated to investigate the potential applications of ZrO₂ nanostructures in optoelectronic devices.