An estimated 1,200 United fans made the trip to Rome to watch the game on Wednesday evening.
"It appears there was trouble outside the stadium," a Foreign Office spokesman said.
"A number of British fans were injured and two British nationals have been arrested.
"Our consular officials are on the way to the hospital to check on conditions, the numbers involved and whether anyone needs assistance.
"The situation is now said to be calm both outside and inside the stadium."