  We study the Dirichlet Casimir effect for a complex scalar field on two
noncommutative spatial coordinates plus a commutative time. To that end, we
introduce Dirichlet-like boundary conditions on a curve contained in the
spatial plane, in such a way that the correct commutative limit can be reached.
We evaluate the resulting Casimir energy for two different curves: (a) Two
parallel lines separated by a distance $L$, and (b) a circle of radius $R$. In
the first case, the resulting Casimir energy agrees exactly with the one
corresponding to the commutative case, regardless of the values of $L$ and of
the noncommutativity scale $\theta$, while for the latter the commutative
behaviour is only recovered when $R >> \sqrt{\theta}$. Outside of that regime,
the dependence of the energy with $R$ is substantially changed due to
noncommutative corrections, becoming regular for $R \to 0$.
