The clashes occurred outside Athens' Olympic Stadium, both before and during the match.
Riot police used pepper spray and stun grenades against hundreds of Greek fans as they tried to break through a police cordon. The youths hurled rocks and petrol bombs at the police.
Earlier, police had intervened to separate rival fans before the game started.
The three fans hurt in those incidents received first aid and their injuries were not considered serious.
Panathinaikos and Lazio are playing in Group J of the European competition, along with Tottenham and Maribor.