Mourinho, who on Thursday was charged over comments he made about referee Anthony Taylor, was sent to the Old Trafford stands by Mark Clattenburg.
He is accused of using abusive or insulting words to the officials in or around the tunnel area at half-time.
He has until Friday to respond.
The FA have acted after considering Clattenburg’s match report – possible punishments include a warning, fine, touchline ban or stadium ban.
Mourinho appeared to be upset when United were not awarded a penalty during Saturday’s match, after Jon Flanagan challenged Matteo Darmian inside the Burnley box.
The 53-year-old emerged for the second half but was escorted to a seat in the stands before being moved a second time, this time to the directors’ box. He declined to speak to the media after the match.
United are eighth in the Premier League and without a win in their past four games.
Mourinho, 53, had been given a deadline of 18:00 GMT on Monday to respond to the first charge, which was issued after the Portuguese said it would be “difficult” for Manchester-based official Taylor to referee United’s game with Liverpool on 17 October.
Managers are not supposed to speak about referees prior to matches.
Mourinho was given a one-match stadium ban and fined £40,000 in November 2015 after the FA backed referee Jon Moss’ claims that the then-Chelsea manager refused to leave the officials’ changing room and verbally abused him and his colleagues at half-time of a defeat at West Ham.
Mourinho was also fined £50,000 for claiming that referees were afraid to award penalties against his side last season after the Blues were beaten 3-1 by Southampton in October.
At the time Mourinho was warned a similar incident over the next 12 months would result in an automatic stadium ban, but that sanction recently expired.