The Black Cats boss was caught off camera threatening to slap BBC reporter Vicki Sparks following the stalemate at the Stadium of Light.
Moyes was forced to apologise for his angry response after Sparks asked whether Moyes was feeling the pressure of owner Ellis Short watching from the stands.
After the official interview finished, 53-year-old Moyes says to Sparks: “It was getting a wee bit naughty at the end there so just watch yourself. You still might get a slap even though you’re a woman.”
The FA statement said: “David Moyes has been charged in relation to comments made after the game against Burnley on 18 March 2017.
“It is alleged the Sunderland manager’s remarks were improper and/or threatening and/or brought the game into disrepute, contrary to FA Rule E3(1).
“He has until 6pm on 3 May 2017 to reply to the charge.”