Tests on Wednesday confirmed the extent of the 31-year-old's injury, which he sustained during a challenge with Sevilla midfielder Gary Medel.
The 31-year-old took a kick from Sevilla's Gary Medel in the first half and had to be replaced as a result, with the club confirming after the match that he had fractured his right forearm.
Following further tests by doctors in the Spanish capital, the club announced that the Portuguese has had a plate fixed to the ulna bone in an effort to repair the damage, with his recovery period as yet unknown.
"[Medel] was going to clear the ball and I put my arm up to protect my face," Tiago recalled to the club's official website. "In the end, I felt something was wrong. I tried to keep playing but I could not continue. The bone was broken and it hurt to move my arm.
"I was feeling pretty good in the team. Injuries never come at a good time and now I have to recover well."
Atletico claimed a 4-3 win over the Andalusians on aggregate, and will face Real Madrid in the final of the competition.