A passive superconducting shield was previously proposed to realize a high-field (above 3 T) septum magnet for the Future Circular Collider proton–proton ring (FCC-hh). This paper presents the experimental results of a potential shield material, MgB $_2$ , at a temperature of 4.2 K. A cylindrical shield with a wall thickness of 8.3 mm was manufactured by the reactive liquid magnesium infiltration technique using extra large grain ( $\sim$ 160 $\mu$ m) boron precursor, and tested in a transverse magnetic field. The shield was stable against flux jumps on the virgin curve, but suffered from flux jumps at low-field levels after high-field exposure. The tube could shield a magnetic field of 2.75 T on its surface before field penetration to its interior. Parameters of the critical current density of the material could be estimated from simulations, which indicate a steeper $J_c(B)$ curve than observed previously for large grain ( $\sim$ 100 $\mu$ m) MgB $_2$ , and predict a slightly better shielding performance (3 T) with an ideal geometry. Relaxation of the shielding currents is at an acceptable level. We estimate that a self-supporting shield of a wall thickness of 14 mm could be adequate for the construction of a 3-T septum magnet, if the flux jump problem can be solved. This thickness would correspond to a total septum thickness (including beam pipes, etc.) of around 22 mm, which is an acceptable figure for the FCC-hh.