Ferguson branded Beck's performance "shocking" after he failed to flag for what the Scot thought was a "clear penalty" for the visitors when Wayne Rooney went down in the box after a challenge by Steven Caulker in Sunday's 1-1 draw at Tottenham.
The United boss said his club had "history" with Beck following his failure to rule out an offside Didier Drogba goal in 2010 and also claimed that: "There was no way we were going to get a decision from (Beck)."
In a statement the FA said that: "It is alleged the Manchester United manager breached FA Rule E3 in that he implied that the match official was motivated by bias.
"Ferguson has until 4pm on Friday 1 February 2013 to respond to the charge."
