The two head coaches appeared to be antagonising one another during the second half of the dramatic Premier League encounter at Stamford Bridge.
On the final whistle, shortly after Harry Kane headed in Spurs' equaliser, Tuchel and Conte shook hands, with the Chelsea boss pulling the Italian back when he did not make eye contact.
This sparked further words being said and several backroom staff from both teams having to separate the two, which resulted in Tuchel and Conte being shown red cards by referee Anthony Taylor.
The FA said in a statement on Monday: "Thomas Tuchel and Antonio Conte have both been charged with a breach of FA Rule E3, following the Premier League fixture between Chelsea FC and Tottenham Hotspur FC on Sunday 14 August 2022.
"It is alleged that the behaviour of both managers was improper following the end of the fixture.
"Thomas Tuchel and Antonio Conte have until Thursday 18 August 2022 to provide their respective responses."
Spurs boss Conte appeared to fan the flames further on Sunday when he took to Instagram to post a story of Tuchel running down the sideline in front of him while celebrating Reece James' goal to make it 2-1 to Chelsea, captioning it: "Lucky I didn't see you… making you trip over would have been well deserved" followed by three laughing emojis.
It is also understood The FA is looking into Tuchel's post-game comments about referee Taylor, whose performance he criticised.
😡 @ChelseaFC boss Thomas Tuchel as gone on a tirade against the referee after @SpursOfficial jagged a late equaliser in a combustible clash at Stamford Bridge.— beIN SPORTS (@beINSPORTS_AUS) August 15, 2022
📰MORE REACTION 👉 https://t.co/Q3U7BqIQmy #PremierLeague #CHETOT pic.twitter.com/hvmqvwvUk0
The FA's investigation will focus on whether Tuchel has brought the game into "disrepute" by implying bias or attacking the integrity of a referee.