We report the fabrication of bio-based thermoplastic polyurethane (TPU) fibrous scaffolds containing essential oils (EO). The main goal of this study was to investigate the effects of essential oil type (St. John’s Wort oil (SJWO), lavender oil (LO), and virgin olive oil (OO))/concentration on the electrospinnability of TPU. The effects of applied voltage, flow rate, and end-tip distance on the diameter, morphology, and wettability of the TPU/EO electrospun fibers were investigated. The electrospun TPU/EO scaffolds were characterized by scanning electron microscopy (SEM), atomic force microscopy (AFM), contact angle (CA), and Fourier transform infrared spectroscopy (FTIR). The addition of oil resulted in an increase in the fiber diameter, reduction in the surface roughness, and, accordingly, a reduction in the contact angle of the composite fibers. TPU fibers containing SJWO and LO have a more flexible structure compared to the fibers containing OO. This comparative study fills the existing information gap and shows the benefits of the fabrication of essential-oil-incorporated electrospun fiber with morphology and size range with respect to the desired applications, which are mostly wound dressing and food packaging.