The skirmishes took place at Piazza della Liberta in the center of the Italian capital where up to 2,500 Lazio fans gathered late Tuesday at the spot of the club's foundation, AFP reported.
The gathering had also been attended by the club's president Claudio Lotito who addressed the crowd but left before tensions mounted.
Shortly after midnight, an estimated 300 fans, with their faces covered, broke away from the main group and began throwing bottles and other objects at police, who responded with tear gas and water cannons.
Police said eight officers had injuries, mostly with cuts and bruising, one fan was arrested and three others detained, all with links to the club's hardcore 'Ultra' fans.
All will receive DASPO Urbano exclusion orders, a 'Sports Event Access Ban'.
Tensions are running high in Italy after violent clashes before Inter Milan's league game against Napoli on December 26 in the San Siro, which was also overshadowed by racist chanting.
A 39-year-old Inter Milan fan was killed after being struck by a car.
There were also clashes in Rome before Lazio's Europa League game against German club Eintracht Frankfurt last month.
Lazio was founded at Piazza della Liberta on January 9, 1900 by a group of army officers.
City rival AS Roma was formed 27 years later following the merger of various capital clubs.