Periodic arrays of apertures with subwavelength dimensions and submicron periodicity were fabricated on gold-coated tips of silica optical fibers using focused ion beam (FIB) milling. Interaction of light with subwavelength structures such as an array of nanoapertures in an optically thick metallic film leads to the excitation of surface plasmon waves at the interfaces of the metallic film and the surrounding media, thereby leading to a significant enhancement of light at certain wavelengths. The spectral position and magnitude of the peaks in the transmission spectra depend on the refractive index of the media surrounding metallic film containing the nanohole array. This lays the foundation for the development of fiber-optic chemical and biological sensors that sense the change in refractive index of the medium around the metallic film. This is demonstrated by testing the sensors with solutions of alcohols with different refractive indices and by the attachment of biomolecules to the sensor surface. The bulk refractive index sensitivity of these nanoaperture array-based sensors is shown to be higher than what has been typically reported for metallic nanoparticle-based plasmonic sensors.