Nanocomposites comprising metal-organic frameworks (MOFs) embedded in a polymeric matrix are promising carriers for drug delivery applications. While understanding the chemical and physical transformations of MOFs during the release of confined drug molecules is challenging, this is central to devising better ways for controlled release of therapeutic agents. Herein, we demonstrate the efficacy of synchrotron microspectroscopy to track the in situ release of 5-fluorouracil (5-FU) anticancer drug molecules from a drug@MOF/polymer composite (5-FU@HKUST-1/polyurethane). Using experimental time-resolved infrared spectra jointly with newly developed density functional theory calculations, we reveal the detailed dynamics of vibrational motions underpinning the dissociation of 5-FU bound to the framework of HKUST-1 upon water exposure. We discover that HKUST-1 creates hydrophilic channels within the hydrophobic polyurethane matrix hence helping to tune drug release rate. The synergy between a hydrophilic MOF with a hydrophobic polymer can be harnessed to engineer a tunable nanocomposite that alleviates the unwanted burst effect commonly encountered in drug delivery.