The two managers shook hands after a 2-2 draw where tempers flared but then faced off on the pitch before being separated by players and staff from both teams.
Both managers were also shown red cards by referee Anthony Taylor as a result of the fracas.
The FA is also investigating Tuchel's comments after the German coach slammed Taylor for his decisions.
Tuchel accused Taylor and the Video Assistant Referee of making wrong decisions which ultimately helped Spurs come away from Stamford Bridge with a point.
