Magnetorheological fluids (MRFs) are smart materials that respond to an external magnetic field by changing their rheological properties. A main drawback of MR fluids is sedimentation which may render the fluids unusable over time. In this study, we introduce a system for the investigation of the sedimentation of magnetorheological fluids in the gravitational field. First of all, differential equation approximations describing the initial stage and the post-saturated stage of the sedimentation are proposed to correlate the experimental results. The custom-developed apparatus is explained, which incorporates a measuring sensor with a lock-in amplifier, a vertically positioned test tube, and a motorized z-axis translating stage. The measurement principle is based on the change of mutual induction between the primary and secondary coils of a sensor, according to the volume fraction-dependent susceptibility. The sensor's coils are driven by a lock-in amplifier, which is able to sense the minor settling distances. The motorized translating axis provides the opportunity for the analysis of the concentration profile of the sample column along its entire length and the device is able to work in fully automated mode. The performance of the device is validated by measurements with Lord MR fluids, for which the sedimentation constant and ratio metrics are provided.