A micro-electro-mechanical system (MEMS) current sensor for sensing a magnetic field produced by an electrical current flowing in a conductor includes a first fixed element and a moving element. The moving element is spaced away from the first fixed element and is movable relative to the fixed element responsive to a magnetic field produced by an electrical current flowing in a conductor for providing a mechanical indication of a strength of the magnetic field. The sensor also includes a tunneling current generator for generating a tunneling current between the first fixed element and the moving element and a tunneling current monitor for monitoring a change in the tunneling current responsive to the mechanical indication to provide an indication of a value of the electrical current in the conductor.