The recently capped Spain international was forced off in the first half of the Rojiblancos' 1-1 draw at Camp Nou but could yet be fit for the return leg at the Vicente Calderon.
The Spain international, who had been a doubt for the quarterfinal first leg with a knee problem, was forced off just 27 minutes into the game at Camp Nou.
Atletico quickly confirmed via its official Twitter account that the forward had suffered "a hamstring muscle injury in his right thigh", immediately prompting fears that the 25-year-old was facing a lengthy spell on the sidelines.
However, the Rojiblancos have now revealed that there was "no tear", meaning Costa could be fit for next week's return leg at the Vicente Calderon.
Costa himself, though, was pessimistic about his chances of facing Barca in the Spanish capital April 9, stating upon his arrival at Atletico's training ground on Wednesday morning that he would not be fit on time.
The Brazil-born attacker is the Rojiblancos' top scorer this season, with 33 goals in 43 games in all competitions.