Drug-loaded core–sheath fibers were successfully prepared from a combination of poly(methyl methacrylate) (PMMA) and polycaprolactone (PCL) using a coaxial electrospinning system and Nimesulide as an anti-inflammatory drug model. An electric field potential of 7–8 kV was found optimal for the formation of the fibers, which were characterized using scanning and transmission electron microscopy techniques combined with attenuated total reflectance infrared spectroscopy and contact angle measurements. Results confirmed the core–sheath morphology and indicated that these fibers are larger in diameter than normal ones (prepared as controls from either PCL or PMMA, under similar conditions). The prepared core–sheath fibers were also investigated by differential scanning calorimetry and thermogravimetric analysis, and results indicated that Nimesulide is completely solubilized in the polymer matrix and that its presence improved the thermal stability of the core–sheath fibers compared to that of normal PMMA fibers. Moreover, PMMA-PCL core–sheath fibers showed an improvement in terms of mechanical properties (such as elongation at break) in comparison with pure PMMA fibers. Drug release studies demonstrated that the delivery of Nimesulide can be modulated by appropriately selecting the loading area, with faster release observed when the drug was located in the sheath. Results suggest altogether the significant potential of PMMA-PCL core–sheath fibers for applications involving delivery of hydrophobic anti-inflammatory drugs such as Nimesulide.