The stab victim was attacked after AS Roma fans boarded a bus taking Arsenal supporters to the Stadio Olimpico, a club spokeswoman said, adding that the victim was not in a life-threatening condition.
The others suffered head injuries in incidents outside the ground.
"Arsenal Football Club and the Metropolitan Police deplore the incident as the safety of our supporters is the highest priority," a statement said.
Violence has marred several Roma matches in Europe in recent years, most prominently in two games against English club Manchester United in 2007.
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