Magnesium oxide nanoclusters have attracted much attention due to their potential applications to catalysis and novel optoelectronic materials. In the present study, we have studied the electronic and magnetic properties of the stoichiometric magnesium oxide nanoclusters (MgO)n for n = 2-20. Although the binding energy increases with the size of the cluster, it reaches the asymptotic limit of about 66.0 eV per unit for relatively large n value. The static dipole polarizability also exhibits distinct size dependence, reflecting clearly the structural transition when the cluster grows. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. Moreover, principle of maximum hardness is also used to characterize the magic number clusters. A well-defined linear correlation is found between static dipole polarizability and the inverse of ionization potential. The most important feature of this work is the NMR study of MgO clusters which is reported for the first time. For each cluster size, the calculated NMR parameters at 17O nuclei together with electronic and structural data provide detailed insight into the properties of bulk and in particular of nanosized structures. Variation of 17O chemical shieldings demonstrates the electrostatic environment divisions around the oxygen nuclei which in turn originate from the cluster structure and its symmetry.