Bundesliga side Leverkusen and Atletico have agreed his surgery will take place in Madrid next week, once Arias can fly.
"We are very sorry for this serious injury and it affects us all. Santiago came to us with great ambitions, this is a heavy blow for him," said Leverkusen sports director Simon Rolfes.
"Like Atletico Madrid, we will do everything possible to support Santiago in his recovery.
"After the operation, he will be in good hands with us in Leverkusen for his rehabilitation."