  In this paper, we prove that Mather-Jacobian (MJ) singularities are preserved
under the process of generic linkage. More precisely, let $X$ be a variety with
MJ-canonical (resp. MJ-log canonical) singularities. Then a generic link of $X$
is also MJ-canonical (resp. MJ-log canonical). This further leads us to a
result on minimal log discrepancies under generic linkage.
