A limited gap between closely spaced structural parts may induce internal pounding in seismically isolated structures, because of notable displacement at the level of the isolation system under severe earthquakes. A gap between a fixed-base elevator shaft and the surrounding building is presented here with reference to a reinforced concrete building located in the Sicilian town of Augusta. The building, comprising a basement and three storeys above the ground level, is seismically isolated at the top of rigid columns in the basement with a hybrid isolation system including elastomeric and sliding bearings, while a steel framed elevator shaft crosses the isolation level. Despite the gap, internal pounding may occur at all levels of the superstructure when the elevator with maximum load stops at the upper floors. To reduce structural pounding effects, a magnetic damped link (MDL) between adjacent corners of the elevator and the surrounding building is proposed. This is obtained as an in parallel combination of an eddy current damped link (ECDL) and an elastic helicoidal spring, and occupies less space than traditional passive dampers and transmits considerably less forces compared to a rigid link configuration. Specifically, an ECDL consists of an outer cylindrical copper tube, as conductor, and an inner tube, equipped with an array of axially magnetized and ring-shaped permanent magnets separated by iron pole pieces, as mover. The relative motion between conductor and magnets, during seismic loading, induces an eddy current producing electromagnetic damping. Given that viscoelastic linear behaviour can be hypothesized for the MDL, a simplified iterative design procedure of the ECDL is proposed, with optimization of the thickness and radius of the magnets, thereby enhancing magnetic flux and energy dissipation. The directionality of the near-fault ground motions is investigated through nonlinear seismic analysis, comparing no connection with four configurations of the interconnection: i.e., flexible and rigid elastic links, viscous and magnetic damped links.