Magnesium oxide (MgO) nanostructures were synthesized by hydrothermal method and investigated for the influence of temperature on the structural and optical properties. Morphological analysis by SEM reveals the formations of nanobelts (NB) and porous nanobelts (PNB). Optical properties were investigated by UV-vis and FTIR spectroscopy. The absorption spectra of MgO NBs and MgO PNBs exhibit a band gap of 3.94 and 4.81 eV, red shifted from bulk. The Verdet constants obtained from Faraday rotation of prepared nanobelts by using polarized lights, and it shows the distinct behavior of MgO nanomaterials.