  We show that the noncommutative Wess-Zumino model is renormalizable to all
orders of perturbation theory. The noncommutative scalar potential by itself is
non-renormalizable but the Yukawa terms demanded by supersymmetry improve the
situation turning the theory into a renormalizable one. As in the commutative
case, there are neither quadratic nor linear divergences. Hence, the IR/UV
mixing does not give rise to quadratic infrared poles.
