© 2016 American Physical Society. Experiments searching for exotic spin-dependent interactions typically employ magnetic shielding between the source of the exotic field and the interrogated spins. We explore the question of what effect magnetic shielding has on detectable signals induced by exotic fields. Our general conclusion is that for common experimental geometries and conditions, magnetic shields should not significantly reduce sensitivity to exotic spin-dependent interactions, especially when the technique of comagnetometry is used. However, exotic fields that couple to electron spin can induce magnetic fields in the interior of shields made of a soft ferromagnetic or ferrimagnetic material. This induced magnetic field must be taken into account in the interpretation of experiments searching for new spin-dependent interactions and raises the possibility of using a flux concentrator inside magnetic shields to amplify exotic spin-dependent signals.