In what has been described as 'a night of shame', fans invaded the pitch on four separate occasions in the Hammers 2-1 win over their fierce rivals.
Players had to be taken off the pitch by officials as news came about that one man had been stabbed and dozens were arrested.
Hammers boss Gianfranco Zola said he had seen nothing like it before.
"I knew it was a game that meant a lot for the two sets of supporters, but I didn't imagine it could be like this," he said.
"I've never seen anything like that after seven years with Chelsea and 11 months with West Ham. I'm sure there will be inquiries and they will try to look at the situation. I was completely shocked."
An FA spokesman said: "We absolutely condemn all of the disorder that has occurred at Upton Park this evening both inside and outside the ground.
"We will be working with all parties including the police and clubs to establish the facts surrounding tonight's events.
"We expect all culprits to be banned from football for life. They have no place in our game."