Torres, 32, was hit from behind by Deportivo's Alex Bergantinos in a clash of heads five minutes from time and hit the ground hard as he appeared to have already lost consciousness.
"Fernando Torres has a traumatic brain injury and has been transferred to hospital for tests," Atletico said in a statement.
"Our player, who is stable, suffered a heavy blow to the head in the final stages of the match and had to be taken quickly to hospital by ambulance.
Players from both sides immediately called for medical attention when Torres hit the ground.
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Distressed Atletico defender Jose Maria Gimenez was seen crying, whilst Deportivo fans gave the former Spanish international a standing ovation as he was carried from the field.
"We are all scared," Atletico left-back Filipe Luis told BeIN Sports.
"The news we have received until now is good. The most important thing is that Fernando is ok."
Atletico had to play out seven minutes of stoppage time with 10 men as they had already made all three substitutions.
Former West Bromwich Albion manager Pepe Mel was making his bow as Deportivo coach after only being hired on Wednesday.
Atletico responded after half-time and equalised in stunning fashion 22 minutes from time when Antoine Griezmann thrashed home a shot from fully 30 yards.