Four were held for breach of the peace while one was detained due to possessing alcohol and resisting arrest.
A further five fans were ejected from the stadium, three of whom have been reported to the procurator fiscal.
About 1,500 Lazio fans are believed to have travelled from Italy for the game. Before the game Lazio fans were filmed appearing to make fascist salutes.
A spokeswoman for Police Scotland confirmed: "We're aware of reports and inquiries are ongoing."