Bisphenol A (BPA) is an endocrine disruptor found in food-contact materials and, even at very low concentrations, poses a serious risk to human health. Therefore, its presence in food should be monitored. Optical fiber sensors are a highly advantageous option for detecting chemical contaminants; however, due to the low concentrations at which these compounds are found, the surface needs to be modified to promote interaction with the target compound. In this work, we present an optical fiber sensor incorporating a microstructured fiber that is sensitive to external media and, therefore, to refractive index variations. To increase sensitivity, the sensor was coated with a chitosan film, a polysaccharide with high biosorbent ability that has been proposed as an effective adsorbent for several contaminants, including BPA. The sensor was then characterized by its response to variations in BPA concentration from 0 to 0.1 mg/mL. The chitosan-coated sensor exhibited a sensitivity over three times higher than that of the uncoated sensor, with a resolution of 9.98 × 10−4 mg/mL. Washing assays revealed that, although the coating cannot be fully regenerated, the sensor can be reused without requiring a complex or time-consuming procedure.