In space there is no air to which the glass can transfer energy, so it should vibrate forever.
Wouldn't the internal friction of the glass molecules (very slowly) dampen the vibration?
Yes, it would lose energy due to that. But then it would gain vibrational heat energy between molecules, which it would have to lose in order to stop "vibrating" completely. It would do this by radiation, but very slowly until it eventually reached a point near absolute zero at which it was in equilibrium: energy received via radiation = energy lost via radiation. It wouldn't really be ringing in a classical sense anymore, but would still have some energy.