  We construct a noncommutative K\"ahler manifold based on a non-linear
perturbations of Moyal integrable deformations of $D=4$ self-dual gravity. The
deformed K\"ahler manifold preserves all the properties of the commutative one,
and we obtain the associated noncommutative K\"ahler potential using the Moyal
deformed gravity approach. We apply this construction to the Atiyah-Hitchin
metric and its K\"ahler potential, which is useful in the description of
interactions among magnetic monopoles at low energies.
