A fast-response optical fiber sensor is designed and fabricated to detect different concentrations of volatile acetone. The proposed sensor structure was fabricated by splicing a segment of tapered coreless fiber (CLF) amid two single-mode fibers (SMF). Herein, tuned tapered diameters and lengths of CLF’s cladding were immersed in various concentrations of the acetone solutions to sense the effective refractive index (RI) variations. Accordingly, the sensor’s performance with tuned diameters at different lengths of the CLF was optimized to realize the suitable size of amplified evanescent fields. The sensor responded remarkably towards acetone concentrations, with a superior sensitivity of 336.102 nm/RIU, 0.163 nm/%, and 27.531 × 10−5 nm/ppm at 5 cm length and 60 µm taper diameter of CLF. The examined sensor possesses a fast response time with a minimum detection limit of 0.244 RIU, 5.025%vol, and 2.9 ppm. Though the rapid evaporation (volatility) of the acetone compound exempted it from air pollutants, many industrial and human body processes produce acetone which needs to be detected. The examined sensor may have the potential to detect in a non-invasive approach with high accuracy and rapid diabetes in humans, lung cancer, etc.