We have developed a non-destructive three-dimensional beam-profile monitor for storage rings. It allows the measurement of the complete profile of stored ion beams by simultaneously detecting electrons and ions created through ionisation of the residual gas. The horizontal coordinate of each point in the profile is determined by detecting the ionised electrons, guided in a strong magnetic field, on a two-dimensional position sensitive detector. The magnetic field assures precision in the determination of the absolute horizontal position of the ion beam and prevents the detection of background electrons originating outside the monitor's active volume. Simultaneously, the vertical coordinate of the beam distribution is obtained by measuring the time difference between the detection of the electrons and the recoil ions in coincidence. The time of flight spectrum shows the different components of the residual gas and allows an intrinsic calibration of the physical parameters. We present results of a test performed with an 8 MeV/u D + beam at the storage ring CRYRING in Stockholm.