Extensive volcanism and high-temperature lavas hint at a global magma reservoir in Io, but no direct evidence has been available. We exploited Jupiter's rotating magnetic field as a sounding signal and show that the magnetometer data collected by the Galileo spacecraft near Io provide evidence of electromagnetic induction from a global conducting layer. We demonstrate that a completely solid mantle provides insufficient response to explain the magnetometer observations, but a global subsurface magma layer with a thickness of over 50 kilometers and a rock melt fraction of 20% or more is fully consistent with the observations. We also place a stronger upper limit of about 110 nanoteslas (surface equatorial field) on the dynamo dipolar field generated inside Io.