There has been violence involving West Ham fans since they moved into their new home at the start of the season.
There was a heavy police presence at the London Stadium, formerly the Olympic Stadium, where there has been violence involving West Ham fans since they moved into their new home at the start of the season.
But skirmishes broke out towards the end of West Ham's 2-1 win, with police and stewards battling to keep supporters apart as coins, bottles and plastic seats were thrown.
"West Ham United and London Stadium partners unreservedly condemn the behaviour of individuals involved in incidents during this evening's fixture with Chelsea," West Ham said in a statement.
"Whilst quickly brought under control, the club, in line with its clear zero-tolerance policy, will work closely with London Stadium, the Metropolitan Police Service and Chelsea to identify the individuals involved.
"Once identified, those found to have acted improperly will be banned from attending any West Ham United fixtures for life and we will request the courts serve banning orders to prevent these individuals attending any other football."
A Chelsea spokesman said: "The club is extremely disappointed to see disturbances at the end of tonight's game and we condemn such behaviour.
"I'm unable to comment further until tonight's incidents have been investigated properly."
West Ham manager Slaven Bilic condemned the violence, which overshadowed a fine performance by his team.
"I noticed it, of course," said the former Croatia defender, whose side will visit Manchester United in the quarter-finals.
"The game was on. I was more concentrated (on that). I don't know what happened. But whatever happened, we are totally against it as a club, as a team.
"For those kind of things to happen, especially in England, is unacceptable."
Chelsea manager Antonio Conte said: "I must be honest, because I didn't see the situation. We were playing and I didn't see this.
"I don't like this type of situation. It's important to see always the right atmosphere.
"Above all in England, we are used to see the right atmosphere. This country is fantastic in this aspect. I'm sorry about this situation."