  We introduce the fibred toric varieties as equivariant $\mathbb{C}P^r$
bundles over lower dimensional toric varieties. An equivalent characterization
is that the natural morphisms on them degenerate to bundle projections in the
context of variation of toric varieties as GIT quotients. Our main observation
is that these fibred toric varieties also arise naturally in the variation of
hyperk\"{a}hler varieties, namely, the fibred toric varieties are contained in
the exceptional sets of the hyperk\"{a}hler natural morphisms and the Mukai
flops.
