The Spurs manager approached the official at full-time, entering the pitch and appearing visibly angry as he spoke to Dean, continuing his tirade even after being told to walk away.
Spurs were angry about a decision to award a corner to Burnley from which Chris Wood opened the scoring, though Pochettino accepted after the match that he had "made a mistake" in confronting the referee.
An FA statement read: "Mauricio Pochettino has been charged with two breaches of FA Rule E3 following the game against Burnley on Saturday.
"It is alleged the Tottenham Hotspur manager's language and/or behaviour at the end of the fixture – both on the pitch and in or around the tunnel area – amounted to improper conduct.
"He has until 18:00 [GMT] on 28 February 2019 to respond to the charge."
The defeat provided a huge blow to Spurs' title hopes and they are six points adrift of Premier League leaders Liverpool.
Speaking after the game, the Argentine accepted that he was wrong to confront the officials, saying emotion got the better of him.
"We made mistakes on the pitch and I made a mistake after. Maybe I needed to go straight away to my dressing room and get some water and be a little bit relaxed," he said.
"I'm not going to talk too much. If we need to justify our defeat it’s to see inside ourselves and that is the reason why we lost the game."
He added: "It's weird, maybe the cables crossed in my brain. I was always under control but what happened there, happened on the pitch. I need to find the reason now that we lost the game, not to find some excuse.
"The first person I have to blame is myself. I said we needed to put pressure on our opponent. In the end we wanted to win and it was because of the emotion."
Spurs will look to rebound in Wednesday's clash with London rivals Chelsea, a match Dean was due to be a fourth official in, but he will now be on the touchline for Manchester City's contest with West Ham.