Ferguson failed to speak to the media after the last-16 second leg in which Nani was given a controversial red card as United lost 2-1 at Old Trafford to go out of the competition 3-2 on aggregate.
In a statement issued on Friday, UEFA said: "Manchester United FC midfield player Nani has been suspended for one match by UEFA's Control and Disciplinary Body, following the red card he received at the UEFA Champions League round of 16 second leg against Real Madrid CF at Old Trafford on 5 March.
"Manchester United head coach Sir Alex Ferguson has been fined €10,000 for non-fulfilment of the post-match media obligations at the same match."
Nani was sent off in the 56th minute with United winning 1-0 and looking as if they were going to win the match.
The red card, shown by Turkish referee Cuneyt Cakir for a high challenge on Real defender Alvaro Arbeloa, turned the course of the game with Real winning thanks to goals from Luka Modric and Cristiano Ronaldo.
Ferguson was incensed by the decision, storming from his seat in the stands to remonstrate with the officials as Nani walked. His assistant Mike Phelan said he was too distraught to talk to the press.
Nani will miss United's first Champions League match next term or his first European game with a new club if he moves.