We present a highly sensitive Lorentz-force magnetic micro-sensor capable of measuring low field values. The magnetometer consists of a silicon micro-beam sandwiched between two electrodes to electrostatically induce in-plane vibration and to detect the output current. The method is based on measuring the resonance frequency of the micro-beam around the buckling zone to sense out-of-plane magnetic fields. When biased with a current of 0.91 mA (around buckling), the device has a measured sensitivity of 11.6 T-1, which is five orders of magnitude larger than the state-of-the-art. The measured minimum detectable magnetic field and the estimated resolution of the proposed magnetic sensor are 100 µT and 13.6 µT.Hz-1/2, respectively. An analytical model is developed based on the Euler-Bernoulli beam theory and the Galerkin discretization to understand and verify the micro-sensor performance. Good agreement is shown between analytical results and experimental data. Furthermore, the presented magnetometer is promising for measuring very weak biomagnetic fields.