The bar is frequented by AS Roma supporters.
The victim suffered a wound to the abdomen and is not in a life-threatening condition, the sources said.
The bar’s owner also suffered minor injuries after the ultras attacked the bar with clubs and damaged property before fleeing by the time the police arrived.
Police are investigating to find the culprits.
Roma midfielder Edoardo Bove was hit by a bottle thrown from the stands during the match, which Lazio won 1-0 to reach the semi-finals of the Cup.
Before the game, a group of Lazio fans made Fascist salutes in the area of the Milvian Bridge.
Fascist salutes made by far-right militants at Sunday’s commemoration for the 1978 Acca Larentia massacre in Rome have sparked a major furore.
Over 100 people have been identified in relation to the salutes made by participants commemorating the 46th anniversary of the Acca Larentia massacre, in which three far-right youth militants died, sources said Wednesday.
ANSA