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We measure the mean halo mass of z ≃ 0.5 Mgii absorbers using the cross-correlation (over comoving scales 0.05-13 h^–1Mpc) between 1806 Mgii quasar absorption systems and ∼250000 luminous red galaxies (LRGs), both selected from the Sloan Digital Sky Survey Data Release 3. The Mgii systems have λ2796 rest-frame equivalent widths W^λ2796_r ≳ 0.3Å. From the ratio of the Mgii-LRG cross-correlation to the LRG-LRG auto-correlation, we find that the bias ratio between Mgii absorbers and LRGs is, which implies that the absorber host galaxies have a mean halo mass ∼20-40 times smaller than that of the LRGs; the Mgii absorbers have haloes of mean mass <logM_h(M_☉)> = 11.94±0.31(stat)^+0.24_–0.25 (sys). We demonstrate that this statistical technique, which does not require any spectroscopic follow-up, does not suffer from contaminants such as stars or foreground and background galaxies. Finally, we find that the absorber halo mass is anticorrelated with the equivalent width. If Mgii absorbers were virialized in galaxy haloes, a positive M_h-W^λ2796_r correlation would have been observed since W^λ2796_ris a direct measure of the velocity spread of the Mgii subcomponents. Thus, our results demonstrate that the individual clouds of a Mgii system are not virialized in the gaseous haloes of the host galaxies. We review past results in the literature on the statistics of Mgii absorbers and find that they too require a M_h-W^λ2796_ranticorrelation. When combined with measurements of the equivalent width distribution (d²N/dz/dW_r), the M_h-W^λ2796_ranticorrelation naturally explains why absorbers with W^λ2796_r≳ 2Å are not seen at large impact parameters. We interpret the M_h-W^λ2796_r anticorrelation within the starburst scenario where strong Mgii absorbers are produced by supernovae-driven winds.