Position sensing with resolution down to the scale of a single atom is of key importance in nanoscale science and engineering. However, only optical-sensing methods are currently capable of non-contact sensing at such resolution over a high bandwidth. Here, we report a new non-contact, non-optical position-sensing concept based on detecting changes in a high-gradient magnetic field of a microscale magnetic dipole by means of spintronic sensors. Experimental measurements show a sensitivity of up to 40 Ω/μm, a linear range greater than 10 μm and a noise floor of 0.5 pm/√[Hz]. Also shown is the use of the sensor for position measurements for closed-loop control of a high-speed atomic force microscope with a frame rate of more than 1 frame/s.