We investigate self-dual MRD codes. In particular we prove that a Gabidulin code in $(\mathbb{F}_q)^{n\times n}$ is equivalent to a self-dual codeif and only if its dimension is $n^2/2$,$n \equiv 2 \pmod 4$, and $q \equiv 3 \pmod 4$. On the way we determine the full automorphism group of Gabidulin codes in $(\mathbb{F}_q)^{n\times n}$.
