  A new class of Riemannian metrics, called octonionic K\"ahler, is introduced
and studied on a certain class of 16-dimensional manifolds. It is an octonionic
analogue of K\"ahler metrics on complex manifolds and of HKT-metrics of
hypercomplex manifolds. Then for this class of metrics an octonionic version of
the Monge-Amp\`ere equation is introduced and solved under appropriate
assumptions. The latter result is an octonionic version of the Calabi-Yau
theorem from K\"ahler geometry.
