Organic–inorganic hybrids represent a good solution to improve the solubility and dissolution rates of poorly soluble drugs whose number has been increasing in the last few years. One of the most diffused inorganic matrices is hydroxyapatite (HAP), which is a biocompatible and osteoconductive material. However, the understanding of the hybrids’ functioning mechanisms is in many cases limited; thus, thorough physicochemical characterizations are needed. In the present paper, we prepared hybrids of pure and Mg-doped hydroxyapatite with meloxicam, a drug pertaining to the Biopharmaceutical Classification System (BCS) class II, i.e., drugs with low solubility and high permeability. The hybrids’ formation was demonstrated by FT-IR, which suggested electrostatic interactions between HAP and drug. The substitution of Mg in the HAP structure mainly produced a structural disorder and a reduction in crystallite sizes. The surface area of HAP increased after Mg doping from 82 to 103 m2g−1 as well as the pore volume, justifying the slightly high drug amount adsorbed by the Mg hybrid. Notwithstanding the low drug loading on the hybrids, the solubility, dissolution profiles and wettability markedly improved with respect to the drug alone, particularly for the Mg doped one, which was probably due to the main distribution of the drug on the HAP surface.