The melt zone in the volcanically active satellite Io plays a key role in diverse processes such as volcanism, heat transfer, tidal dissipation, and the orbital evolution of the Galilean satellites in the Laplace resonance. Information on the melt distribution, the degree of partial melt, and the possible existence of a global magma ocean has been derived from Galileo magnetic induction measurements, volcanic eruption temperatures, and Hubble Space Telescope auroral spot observations but is currently inconclusive. Here, we calculate the libration amplitude of Io for a diverse set of internal structure models and show that Io's libration can provide insight into the existence of a global magma ocean and into the thickness and rigidity of the crust above it. The diurnal libration amplitude of Io is several times larger if Io has a magma ocean instead of a partial melt asthenosphere and can reach values of above 1 km, making it easily observable for spacecraft flying close by Io on multiple occasions. It also strongly increases with decreasing crustal thickness and increases significantly with increasing rigidity. We demonstrate that the combination of observations of the libration amplitude and the tidal Love number k2 will allow estimating the rigidity and thickness of the crust separately, which is impossible with only one of the quantities observed.