In this paper, magnetic fluid (MF), a new type of optical functional nanomaterial with interesting optical characteristics under the external magnetic field, is adopted to form a novel fiber-optic magnetic field sensor. The proposed sensor is based on Mach-Zehnder interferometer (MZI) and has a multimode-singlemode-multimode (MSM) fiber structure. The MSM structure was fabricated by splicing a section of uncoated single mode fiber (SMF) between two short sections of multimode fibers (MMFs) using a fiber fusion splicer. The magnetic field sensing probe was made by inserting the fiber-optic structure in an MF-filled capillary tube. Variations in an external magnetic field is seen to cause changes in the refractive index of MF. This tunable change in the refractive index with magnetic field strengths between 0.6 mT to 21.4 mT produces a shift in the peak position of the wavelength. The shift of the valley wavelength with magnetic field intensity has a good linearity of up to 99.6%. The achieved sensitivity of the proposed magnetic field sensor is 0.123 nm/mT, which is improved by several folds compared with those of most of the other reported MF-based magnetic field sensors. Furthermore, we build the corresponding circuit-based measurement system, and the experimental results show that the voltage change indirectly reflects the change of the external magnetic field strength. Therefore, this provides the potential to fiber-based magnetic field sensing applications.