Two supporters were kept in overnight and a local hospital spokesman said one fan had suffered stomach wounds as 10-man United lost their quarter-final, first leg 2-1.
"Eleven Britons were treated in hospital. Only two stayed overnight and one of them is out already," a British Embassy spokeswoman said on Thursday. She added that the condition of the supporter still in hospital was not life-threatening.
UEFA, European soccer's governing body, said it would open an investigation into the events in Rome.
"We're waiting for the reports -- from the match delegate, the referee and the security officer -- and the documentation. We will also be looking at video footage and images," a UEFA spokesman said on Thursday.
Trouble began inside the Olympic stadium after Roma took the lead just before halftime when rival fans traded insults and threw objects from one section of the ground to the other.
Television pictures showed Italian police flailing at United supporters with batons, leaving several of the English club's fans bleeding profusely from head wounds.
One policeman was shown raining blows on a supporter who lay motionless on the ground.
The British Embassy said more than 11 fans were injured, with local media putting the number at 18. Italian police could not confirm the number injured, pending their own investigation.
One United supporters club said it would send a statement to UEFA and asked fans for eyewitness accounts of the clashes.
"The Italian police were stationed on our side of the fence, in attack formation against United fans, in a way that only made sense if they were trying to protect the Roma fans from us," the Independent Manchester United Supporters' Association said on its Web site.
"There is something very wrong here and IMUSA aims to get to the bottom of it."
United warned fans before the match that they might be attacked in Rome, prompting a rebuke from the city's mayor and Roma's coach Luciano Spalletti.
(Additional reporting by Trevor Huggins in London)