The developments are in reaction to Tuesday's Champions League match with Real Madrid.
Manager Sir Alex Ferguson reacted angrily after Nani was sent off for a high challenge on Madrid's Alvaro Arbeloa in the 56th minute of the match, which United were leading 1-0 at the time.
But with the man advantage, Madrid came back to win 2-1 on the night, 3-2 on aggregate.
Ferguson did not appear for interviews after the match, with his assistant Mike Phelan attending the post-match press conference and saying the manager was too "distraught" to speak, while the players did not stop to talk in the mixed zone.
UEFA issued a short statement Wednesday confirming disciplinary proceedings have been opened against the club regarding the two incidents.
"The case will be dealt with by the UEFA Control and Disciplinary Body on Thursday 21 March," the statement said.
Champions League rules oblige managers to speak to the media after every match.
Phelan had suggested he was at least likely to adopt a more diplomatic stance than his boss, who might have risked an even heavier sanction had he said in public what he thought in private.
Wednesday's statement from UEFA made no mention of defender Rio Ferdinand, who sarcastically applauded Turkish referee Cuneyt Cakir after the final whistle when the players surrounded the officials.
UEFA has already released a statement insisting it had no issues regarding Cakir's performance.
"There are no issues for us regarding the sending off," said a UEFA spokesman.
Ferguson is due to speak to the media on Friday ahead of Manchester United's FA Cup quarter-final with Chelsea.
There has been an element of circling the wagons at Old Trafford, with former captain Roy Keane's suggestion that Nani deserved his punishment for a high tackle on Alvaro Arbeloa coming in for stinging criticism.
Former United European Cup winner Paddy Crerand was particularly venomous, although others were equally incredulous.
"That decision was an absolute joke," former United defender Viv Anderson said.
"The players will feel as though they have been cheated by the referee."
Another ex-player, Lou Macari, said: "He was the same referee who sent John Terry off in the semi-final last season.
"When I read that I thought surely he is not going to be one of those who brings out yellow cards for fun.
"He brought a red out for fun instead."
Once his anger has subsided, Ferguson will be able to reflect on an outstanding first hour in which Danny Welbeck and Ryan Giggs were superb.
However, should the United boss watch the match again, he may concede Rafael could easily have been sent off for a handball on the line.
He may also wonder at the speed with which Real adjusted to their numerical advantage, turning the entire tie on its head before United sorted themselves out.
As Phelan pointed out, United are used to recovering from such shattering reversals of fortune and Sunday's FA Cup quarter-final with Chelsea is almost perfect, given the Red Devils have home advantage against a side mired in their own problems and tired by a midweek trip to Romania.
And although Europe remains the pinnacle, a fourth domestic league and cup double would be welcomed with open arms at Old Trafford.
However, if it all goes wrong for Ferguson's team, a season that promised so much will suddenly not appear quite so positive, given the general acceptance that a 20th championship is already secure.
"If you are in the next round of the Champions League, all the pressure for Sunday is off," said Macari.
"You get knocked out of the Champions League and suddenly you have a big game on Sunday. It adds a little bit of pressure.
"The players have to go out and deliver.
"It is not a foregone conclusion, though, and all of a sudden, from us talking about the treble, this defeat is an example of why it was silly.
"So many things can go wrong.
"I just hope they can rise to the occasion on Sunday."