Although metal–organic frameworks (MOFs) have widely demonstrated their convenient performances as drug-delivery systems, there is still work to do to fully understand the drug incorporation/delivery processes from these materials. In this work, a combined experimental and computational investigation of the main structural and physicochemical parameters driving drug adsorption/desorption kinetics was carried out. Two model drugs (aspirin and ibuprofen) and three water-stable, biocompatible MOFs (MIL-100(Fe), UiO-66(Zr), and MIL-127(Fe)) have been selected to obtain a variety of drug–matrix couples with different structural and physicochemical characteristics. This study evidenced that the drug-loading and drug-delivery processes are mainly governed by structural parameters (accessibility of the framework and drug volume) as well as the MOF/drug hydrophobic/hydrophilic balance. As a result, the delivery of the drug under simulated cutaneous conditions (aqueous media at 37 °C) demonstrated that these systems fulfill the requirements to be used as topical drug-delivery systems, such as released payload between 1 and 7 days. These results highlight the importance of the rational selection of MOFs, evidencing the effect of geometrical and chemical parameters of both the MOF and the drug on the drug adsorption and release.