United goalkeeper David De Gea appeared to be targeted by water bottles from a section of the West Ham support.
The FA said: “We will work closely with both clubs and the Metropolitan Police to fully investigate these matters.”
Manchester United manager Louis van Gaal added: “I think the images shall tell everything.
“It has an influence on the players – not just Manchester United, but also West Ham. I think it will be very aggressive because the fans were emotional. They will influence the game, I think.”
West Ham co-Chairman David Sullivan played down the incident, telling BBC Radio 5 live that their opponents should have arrived earlier.
“I don’t understand why United couldn’t get here at 4pm. They could have got here early. They knew it would be busy. It’s crazy.
“There was congestion in the street and they couldn’t get the coach in. There were people around the coach, but there was no attack on the coach.
A Metropolitan Police spokesman said an “appropriate policing plan is in place”, adding: “We are aware that a number of items were thrown towards Manchester United’s coach.
“One police officer and a member of the public sustained minor injuries. There have been no arrests.”
Jonathan Pearce, the BBC’s commentator at Upton Park, said: “It is a terrible, terrible shame. The bottles were thrown just across the road from the iconic statue of World Cup winners [Geoff] Hurst, [Bobby] Moore and [Martin] Peters.
“So many wonderful West Ham fans are here and they have been denied a perfect evening.”
BBC Sport’s chief football writer Phil McNulty, also at the game, said: “Manchester United arrived late, as they did for the recent London game at Tottenham, and were met by thousands of West Ham United fans thronging around near the entrance to the stadium.
“It was then that the attack on the team coach, as confirmed by United captain Wayne Rooney, took place.
“Some of the behaviour of supporters outside has taken the edge of the celebratory tone of the occasion.”