Simeone has been punished after being dismissed from the bench following an ugly on-field spat with Real defender Raphael Varane just before the final whistle of his side's 4-1 defeat in Lisbon.
Varane appeared to kick the ball towards Simeone as he walked back after Cristiano Ronaldo's penalty towards the end of extra-time and, after whacking it back at him, Simeone stormed on the the field and had to be restrained as he went for the player.
Alonso, meanwhile, had been given a ban for a "breach of general principles of conduct" for his actions during the final.
The Spain international was banned for the match and as such could not be on the bench but, when Gareth Bale scored to put Real 2-1 ahead in extra-time, he ran down the touchline to join his team-mates in celebration.
Alonso will serve his ban during next month's UEFA Super Cup final against Sevilla.
Both clubs have also been fined for picking up five or more yellow cards in the game as well as for their supporters setting off fireworks, with Atletico - who had seven players booked - having to pay 21,000 euros (£16,600) and Real 18,000 euros (£14,200).
A UEFA statement read: "The UEFA Control, Ethics and Disciplinary Body has today announced decisions following disciplinary proceedings which were opened after the 2014 UEFA Champions League final in Lisbon between Real Madrid and Atletico Madrid on 24 May.
"Atletico de Madrid: Head coach Diego Simeone will be suspended for the next UEFA competition match in which he would participate (dismissal from bench).
"The club has been fined 21,000 euros for the improper conduct of the team (5 cards or more, Art. 15 (4) DR) and improper conduct of their supporters (setting-off of fireworks, Art. 16 (2)).
"Real Madrid: Xabi Alonso will be suspended for the next UEFA competition match for which he will be eligible. This suspension is to be served during the UEFA Super Cup final between Real Madrid and Sevilla FC on 12 August 2014 (breach of general principles of conduct, Art. 11 DR).
"The club has been fined 18,000 euros for the improper conduct of the team (5 cards or more, Art. 15 (4) DR) and improper conduct of their supporters (setting off of fireworks, Art. 16 (2) DR))."
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