Costa was forced off after 30 minutes of Tuesday's Champions League quarter-final, first leg at Barcelona, which ended 1-1, when he pulled up clutching the back of his leg.
Atletico said on their Twitter feed tests had revealed a muscle strain instead of a tear. The club did not specify how long he might be out of action but local media said seven days and suggested he might be available for the return leg at the Calderon next Wednesday.
Costa had scored seven goals in five appearances in this season's Champions League before Tuesday and has 25 in 30 La Liga outings.
Atletico coach Diego Simeone told a news conference after the match at the Nou Camp that Raul Garcia, David Villa or Adrian were ready to stand in for the Spain international.
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