We study the hydrodynamic expansion of a rotating strongly interacting Fermi gas by releasing a cigar-shaped cloud with a known angular momentum from an optical trap. As the aspect ratio of the expanding cloud approaches unity, the angular velocity increases, indicating quenching of the moment of inertia I to as low as 0.05 of the rigid body value I(rig). Remarkably, we observe this behavior in both the superfluid and collisional normal fluid regimes, which obey nearly identical zero-viscosity irrotational hydrodynamics. We attribute irrotational flow in the normal fluid to a decay of the rotational part of the stream velocity during expansion, which occurs when the shear viscosity is negligible. Using conservation of angular momentum, we directly observe a fundamental result of irrotational hydrodynamics, I/I(rig) = delta2, where delta is the deformation parameter of the cloud.