A magnetic field sensor may include a semiconductor structure having a planar surface, and first, second, and third sensing devices. The semiconductor structure may include a semiconductor member having a two-dimensional electron gas therein, and an insulator member disposed on the semiconductor member. The first sensing device may be configured to sense magnetic field along a first axis parallel to the planar surface. The second sensing device may be configured to sense magnetic field along a second axis parallel to the planar surface, and orthogonal to the first axis. The third sensing device may be configured to sense a magnetic field along a third axis normal to the planar surface. Each of the first, second, and third sensing devices may be formed in the semiconductor structure and may include electrodes that extend from the insulator member to the two-dimensional electron gas.