We predict the strong enhancement in the photoabsorption of small Mg clustersin the region of 4-5 eV due to the resonant excitation of the plasmon oscillations of cluster electrons. The photoabsorption spectra for neutral Mg clusters consisting of up to N=11 atoms have been calculated using ab initio framework based on the time dependent density functional theory (TDDFT). The nature of predicted resonances has been elucidated by comparison of the results of the ab initio calculations with the results of the classical Mie theory. The splitting of the plasmon resonances caused by the cluster deformation is analysed. The reliability of the used calculation scheme has been proved by performing the test calculation for a number of sodium clusters and the comparison of the results obtained with the results of other methods and experiment.