In this paper, a high-sensitivity magnetic field sensor based on a single-mode–tapered small-core–single-mode (STSCS) optical fibre structure is investigated. The tapered small-core section of STSCS is surrounded by magnetic fluid (MF) containing ferromagnetic particles (FMPs) of different concentrations. The FMPs align themselves along the magnetic field, depending on the strength of the magnetic field. This alignment of FMPs changes the refractive index around the tapered small-core section, which in turn changes the output spectral response of the STSCS optical fibre structure. The change in spectral response is then calibrated for sensing the magnetic field strength. This paper also investigates the effect of both the taper waist diameter of the STSCS optical fibre structure and the concentration of MF surrounding it on the magnetic field sensitivity. The maximum sensitivity demonstrated in this paper is 0.46 nm/mT for a taper waist diameter of 10 μm surrounded by 1.22% FMPs in the MF. The magnetic sensor demonstrates reversible results, and its effects on the orientation of the magnetic field along the X–Y, X–Z and Y–Z axes are also investigated, which suggest that the sensor is capable of vector magnetic field measurement.