We demonstrate a high-sensitivity fiber-optic magnetic field sensor, which consists of a cladding-etched long-period fiber grating (LPFG) near the dispersion turning point (DTP) integrated with a magnetic fluid (MF). By reducing the cladding diameter of the LPFG, the fundamental mode is coupled to the lowest order cladding mode (LP0,2) near the DTP, which has a much higher surrounding refractive index sensitivity. Thanks to the excellent magneto-optical characteristics of the MF, the proposed sensor can achieve a magnetic field intensity sensitivity of 44.69 nm/mT in the range of 3-7.4 mT. The minimum magnetic field intensity that can be detected is 0.45 µT due to the 0.02-nm wavelength resolution of the optical spectrum analyzer. The proposed etched DTP-LPFG-based sensor with ultrahigh magnetic field sensitivity could have potential applications in magnetic fields and electrical systems.