Seven fans have been injured, some suffering knife wounds, in clashes between supporters of Lazio and Roma.
La Repubblica said three people were stabbed, and one was hospitalized in a serious condition with a throat wound. The reports said four people have been arrested.
Roma beat Lazio 2-1 on Sunday to reclaim the Serie A lead.
Police had to intervene inside the Stadio Olimpico before the match as fans battled each other in the stands.
The start of the match was brought forward by two hours due to security concerns.
When the clubs met in December, the game was suspended for nearly 10 minutes during the first half due to firecrackers exploding in the stands.
Meanwhile, Roma forward Mirko Vucinic, who scored both goals for the Serie A leaders, was delighted with the result.
“Winning a derby is fantastic. It is not important who scores the goals, but scoring a double that happend to be decisive is out of this world,” Vucinic said afetrwards.
“It went well for us, and even if [Lazio attacker Sergio] Floccari had of scored for a 2-0 lead, who knows how the match could have ended.
“The important thing was that we won because Inter had put lots of pressure on us, and we are accustomed to staying on top,” he added.