The officer is being treated for a damaged spleen as he tried to control fights between rival sets of fans prior to the game at Parma, which the Nerazzurri won 2-0.
Another officer was also injured after he was hit by a rock which broke a van's window.
Inter fans had been banned from attending the match for safety reasons but descended on Parma en masse and over 1,000 fans still managed to gain entry to the match.
The majority of the clashes broke out when fans without tickets tried to get into the Stadio Ennio Tardini by climbing over fences.
Nerazzurri supporters also heavily damaged a school outside the stadium after the match, breaking windows and tearing up trees.
Violence also touched Scudetto rivals Roma's match at Catania, with the home fans breaking a window of the Giallorossi's team bus.