  We study the Mumford--Tate conjecture for hyperk\"{a}hler varieties. We show
that the full conjecture holds for all varieties deformation equivalent to
either an Hilbert scheme of points on a K3 surface or to O'Grady's ten
dimensional example, and all of their self-products. For an arbitrary
hyperk\"{a}hler variety whose second Betti number is not 3, we prove the
Mumford--Tate conjecture in every codimension under the assumption that the
K\"{u}nneth components in even degree of its Andr\'{e} motive are abelian. Our
results extend a theorem of Andr\'{e}.
