The Spain international has been handed a one-match ban by Uefa's disciplinary committee for invading the pitch during their 4-1 Champions League final win over Atletico Madrid last season.
Alonso was forced to watch the game against Atletico from the stands due to another suspension after picking up a yellow card in the semi-final clash with Bayern Munich.
He ran onto the pitch, however, after Gareth Bale netted in extra-time to make the score 2-1 and he has now been punished for improper conduct.
Meanwhile, Atletico Madrid coach Diego Simeone has also been handed a one-game touchline ban after he was sent off by referee Bjorn Kuipers in the closing stages of the match.
Simeone ran onto the pitch after Cristiano Ronaldo struck the fourth from the spot and was then involved in a heated exchange with Real defender Raphael Varane.
Additionally, both clubs have also been fined for improper conduct of their players - due to picking up five or more yellow cards in the match - and of their fans for setting off fireworks.
Atletico must pay Uefa £16,600 while Real have been hit with an £14,200 fine.