There were also minor incidents after the match outside the stadium involving supporters from both clubs and the police.
About 500 West Ham followers, many of them based in the United States, were thought to have attended the match. One was arrested for a disorder offence.
"We understand this was an isolated incident leading to one initial arrest that was quickly dealt with by security staff," Scott Duxbury, the West Ham chief executive, said.
"While we take such matters seriously and utterly condemn the actions of those involved, we must not let this mar what has been a positive trip so far and the excellent way we and our supporters have been treated in Columbus. The match was a fitting warm-up for the MLS All-Star Game, which we are proud to be involved in."