Electrospun mats of PLA and PLA/Hap nanofibers produced by electrospinning were loaded with doxycycline (Doxy) through physical adsorption from a solution with initial concentrations of 3 g/L, 7 g/L, and 12 g/L, respectively. The morphological characterization of the produced material was performed using scanning electron microscopy (SEM). The release profiles of Doxy were studied in situ using the differential pulse voltammetry (DPV) electrochemical method on a glassy carbon electrode (GCE) and validated through UV-VIS spectrophotometric measurements. The DPV method has been shown to be a simple, rapid, and advantageous analytical technique for real-time measurements, allowing accurate kinetics to be established. The kinetics of the release profiles were compared using model-dependent and model-independent analyses. The diffusion-controlled mechanism of Doxy release from both types of fibers was confirmed by a good fit to the Korsmeyer–Peppas model.