Migraine is now the sixth most common disease in the world and affects approximately 15% of the population. Non-steroidal anti-inflammatory drugs, including ketoprofen, diclofenac sodium, and ibuprofen, are often used during migraine attacks. Unfortunately, their efficiency can be reduced due to poor water solubility and low cellular uptake. This requires the design of appropriate porous carriers, which enable drugs to reach the target site, increase their dissolution and stability, and contribute to a time-dependent specific release mode. In this research, the potential of the MIL-88A metal-organic frameworks with divergent morphologies as diclofenac sodium delivery platforms was demonstrated. Materials were synthesized under different conditions (temperature: 70 and 120 °C; solvent: distilled water or N,N-Dimethylformamide) and characterized using X-ray diffraction, low-temperature nitrogen adsorption/desorption, thermogravimetric analysis, infrared spectroscopy, and scanning electron microscopy. They showed spherical, rod- or diamond-like morphologies influenced by preparation factors. Depending on physicochemical properties, the MIL-88A samples exhibited various sorption capacities toward diclofenac sodium (833–2021 mg/g). Drug adsorption onto the surface of MIL-88A materials primarily relied on the formation of hydrogen bonds, metal coordination, and electrostatic interactions. An in vitro drug release experiment performed at pH 6.8 revealed that diclofenac sodium diffused to phosphate buffer in a controlled manner. The MIL-88A carriers provide a high percentage release of drug in the range of 58–97% after 24 h.