Trouble erupted outside Anfield minutes before kick-off in the first leg of the tie on April 24, with Liverpool fan Sean Cox left in a critical condition following the incident .
UEFA confirmed on Tuesday disciplinary proceedings have been opened against both clubs in connection with clashes between supporters.
Liverpool are additionally under investigation for the throwing of objects and setting off of fireworks during the game.
This case will be dealt with by the UEFA Control, Ethics and Disciplinary Body on May 31.
Jurgen Klopp's Reds face holders Real Madrid in the Champions League final on Saturday in Kiev, having progressed 7-6 on aggregate against Roma.