The incident at Stamford Bridge started when Chelsea forward Joao Pedro reacted to West Ham winger Adama Traore's shove on Blues defender Marc Cucurella in added time.
Ugly scenes followed and Hammers defender Jean-Clair Todibo was shown a straight red card by referee Anthony Taylor for grabbing Joao Pedro by the neck.
The Football Association said: "It was also alleged that West Ham United FC failed to ensure its players didn't behave in an improper and/or provocative and/or violent way at this time.”
"Both clubs subsequently admitted the charges against them."
In imposing the fines, an independent regulatory commission took the fact that both clubs had committed previous breaches of FA Rule E20.1 into account.
The rule states that there should be no behaviour that is "improper, offensive, violent, threatening, abusive, indecent, insulting or provocative".
The commission said both clubs "contributed to the incident" and that Traore's "disproportionate reaction to Mr Cucurella's movement as he returned to his feet, was the catalyst for what occurred".