The Portugal international suffered the problem in training on Thursday and a scan revealed that he had fractured the scaphoid in his left wrist.
Atletico have not released an expected return date following the operation, but it seems certain that he will miss the UEFA Champions League last-16 first leg clash with Milan next Wednesday.
Further to his wrist injury, Tiago is also nursing ligament damage in his right knee after a reckless tackle by compatriot Helder Barbosa in Saturday's 2-0 defeat at Almeria, a loss that also saw Atletico drop from the top of La Liga.
An Atletico statement read: "Tiago Cardoso was operated on early in the morning of Tuesday, February 11th in Clinical Fremap Majadahonda after a scaphoid fracture was detected in the left wrist in the tests which underwent on Sunday at the same hospital.
"The Portuguese midfielder had suffered the discomfort in training last Thursday (February 6).
"Moreover, the player was substituted in Saturday's game in Almeria due to injury 67 minutes after a forceful tackle by Barbosa on his right leg.
"After medical tests, the report detailed the player suffered a 'grade II sprain of the medial collateral ligament in his right knee', to which was added a 'fractured scaphoid of the left wrist without displacement' injury that has been operated on Tuesday."
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