The former Portugal international was injured in a crunching tackle from compatriot Helder Barbosa 67 minutes into Atleti's 2-0 defeat, which saw them toppled from La Liga's summit.
Barbosa was tripped by Diego Ribas as he approached Tiago, landing both feet midway up his opponent's leg.
As a result, Atleti confirmed on Sunday that the former Chelsea midfielder has suffered a "grade II sprain of the medial collateral ligament in his right knee", which could keep him out for up to three months.
To make things worse for Tiago, he also suffered a broken wrist as he fell to the ground.
Tiago has made 17 appearances so far this season, scoring twice - including one in Atleti's 4-2 win over Almeria earlier on this campaign.
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