Neither club will face a points deduction. But Spurs will be hit hardest. They were already facing an automatic £25,000 fine for having nine players booked.
But they will also be fined for each of the three mass confrontations between the sides in the 45th and 87th minutes, and at the end of the game.
Spurs were fined £20,000 in January for failing to control their players during their game with West Brom, and this will also be taken into account.
Chelsea also face fines for all three confrontations – and have already been punished twice this season for similar offences, against West Brom and Arsenal.
Both clubs have until 6pm next Monday to respond to the charges.