Abstract The XQ-100 survey provides optical and near-infrared coverage of 36 blindly selected, intervening damped Lyman α systems (DLAs) at 2 < zabs < 4, simultaneously covering the Mg ii doublet at λλ2796, 2803Å, and the Ly α transition. Using the XQ-100 DLA sample, we investigate the completeness of selecting DLA absorbers based on their Mg ii rest-frame equivalent width ($W_{0}^{2796}$) at these redshifts. Of the 29 DLAs with clean Mg ii profiles, we find that six (20 per cent of DLAs) have $W_{0}^{2796}$ < 0.6 Å. The DLA incidence rate of $W_{0}^{2796}$ < 0.6 Å absorbers is a factor of ∼5 higher than what is seen in z ∼ 1 samples, indicating a potential evolution in the Mg ii properties of DLAs with redshift. All of the $W_{0}^{2796}$ < 0.6 Å DLAs have low metallicities (−2.5 < [M/H] < −1.7), small velocity widths (v90 < 50 km s−1), and tend to have relatively low N(H i). We demonstrate that the exclusion of these low $W_{0}^{2796}$ DLAs results in a higher mean N(H i) which in turn leads to an ∼7 per cent increase in the cosmological gas density of H i of DLAs at 2 < zabs < 4; and that this exclusion has a minimal effect on the H i-weighted mean metallicity.