We have used Galaxy IMage 2D (GIM2D) to quantify the morphological properties of 40 intermediate-redshift Mg ii absorption-selected galaxies [0.03 ≤ Wr(2796) ≤ 2.9 Å], imaged with WFPC-2/Hubble Space Telescope (HST), and compared them to the halo gas properties measured from HIRES/Keck and UVES/VLT quasar spectra. We find that as the quasar–galaxy separation, D, increases the Mg ii equivalent decreases with large scatter, implying that D is not the only physical parameter affecting the distribution and quantity of halo gas. Our main result shows that inclination correlates with Mg ii absorption properties after normalizing out the relationship (and scatter) between the absorption properties and D. We find a 4.3σ correlation between Wr(2796) and galaxy inclination, normalized by impact parameter, i/D. Other measures of absorption optical depth also correlate with i/D at greater than 3.2σ significance. Overall, this result suggests that Mg ii gas has a co-planer geometry, not necessarily disc-like, that is coupled to the galaxy inclination. It is plausible that the absorbing gas arises from tidal streams, satellites, filaments, etc., which tend to have somewhat co-planer distributions. This result does not support a picture in which Mg ii absorbers with Wr(2796) ≲ 1 Å are predominantly produced by star formation driven winds. We further find that: (1) Mg ii host galaxies have quantitatively similar bulge and disc scalelength distribution to field galaxies at similar redshifts and have a mean disc and bulge scalelength of 3.8 and 2.5 kpc, respectively; (2) Galaxy colour and luminosity do not correlate strongly with absorption properties, implying a lack of a connection between host galaxy star formation rates and absorption strength; and (3) parameters such as scalelengths and bulge-to-total ratios do not significantly correlate with the absorption parameters, suggesting that the absorption is independent of galaxy size or mass.