In the present work, the porous metal-organic framework (MOF) Basolite®F300 (Fe-BTC) was tested as a potential drug-releasing depot to enhance the solubility of the anticancer drug paclitaxel (PTX) and to prepare controlled release formulations after its encapsulation in amphiphilic methoxy poly(ethylene glycol)-poly(ε-caprolactone) (mPEG-PCL) nanoparticles. Investigation revealed that drug adsorption in Fe-BTC reached approximately 40%, a relatively high level, and also led to an overall drug amorphization as confirmed by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The dissolution rate of PTX-loaded MOF was substantially enhanced achieving a complete (100%) release within four days, while the neat drug only reached a 13% maximum rate (3–4 days). This PTX-Fe-BTC nanocomposite was further encapsulated into a mPEG-PCL matrix, a typical aliphatic amphiphilic copolyester synthesized in our lab, whose biocompatibility was validated by in vitro cytotoxicity tests toward human umbilical vein endothelial cells (HUVEC). Encapsulation was performed according to the solid-in-oil-in-water emulsion/solvent evaporation technique, resulting in nanoparticles of about 143 nm, slightly larger of those prepared without the pre-adsorption of PTX on Fe-BTC (138 nm, respectively). Transmission electron microscopy (TEM) imaging revealed that spherical nanoparticles with embedded PTX-loaded Fe-BTC nanoparticles were indeed fabricated, with sizes ranging from 80 to 150 nm. Regions of the composite Fe-BTC-PTX system in the infrared (IR) spectrum are identified as signatures of the drug-MOF interaction. The dissolution profiles of all nanoparticles showed an initial burst release, attributed to the drug amount located at the nanoparticles surface or close to it, followed by a steadily and controlled release. This is corroborated by computational analysis that reveals that PTX attaches effectively to Fe-BTC building blocks, but its relatively large size limits diffusion through crystalline regions of Fe-BTC. The dissolution behaviour can be described through a bimodal diffusivity model. The nanoparticles studied could serve as potential chemotherapeutic candidates for PTX delivery.