Two men were arrested on suspicion of affray and a third on suspicion of assaulting a police officer, Scotland Yard said.
Officers were also deployed inside the stadium during the match to deal with a separate disturbance, the Met said.
However, it was “quickly dealt with”, the force said, and no arrests were made.
Police escorted Middlesbrough fans away from the stadium while officers contained some West Ham supporters.
There have been several crowd disturbances since the club moved to the former Olympic Stadium.
At the first Premier League match at the venue – against Bournemouth on 21 August – some fans arrived with tickets for seats that did not exist, while fighting broke out between rival supporters outside the stadium.
West Ham said 10 fans were ejected from the stadium during the 4-2 defeat by Watford last month.
The Met said more than 40,000 people had attended Saturday’s match against Middlesbrough, and the “vast majority” had been good natured.