This work introduces a novel design of a fixture to be adapted to the commercial version of the capillary breakup extensional rheometer (CaBER), here termed as an extensional magneto-rheological fixture (ExMRFx), that allows the characterization of magnetic fluids under uniaxial extensional flow. The fixture consists of four solenoids that generate a homogeneous magnetic field with a tunable intensity on the fluid sample, while characterized in the CaBER under uniaxial extensional flow. The ExMRFx is designed in two configurations, one to impose a magnetic field parallel, while the other to impose a magnetic field perpendicular to the deformation axis. As an example of possible application, the ExMRFx has been tested with a magnetorheological fluid (MRF) consisting of a suspension of carbonyl iron particles dispersed in glycerine. The experimental results show that the filament thinning process of the MRF sample is influenced by the concentration of carbonyl iron particles used, the orientation of the magnetic field (parallel or perpendicular), the intensity of the magnetic field applied, and finally the Hencky strain imposed. Depending on the combination of these latter parameters, the MRF sample may result in a very stable filament bridging the two measuring plates, which will remain stable, as long as none of the experimental parameters change.