A simple refractive index sensor based on a small section of fiber damaged by the fiber fuse is proposed and demonstrated with a sensitivity of 350.58 nm/refractive index unit (RIU). For comparison, a hetero-core structure fiber sensor composed of a short no-core fiber (NCF) sandwiched between two pieces of single-mode fibers is demonstrated with a sensitivity of 157.29 nm/RIU. The fiber fuse technique can allow mass production of sensors by incorporating small sections of the damaged fiber of any type into each device. We believe this is the first application of the periodic damage tracks in optical fibers formed by the fiber fuse.