The Spanish striker, who was forced to leave Saturday's contest in the 90th minute, underwent an MRI that confirmed the injury, Atletico announced on Tuesday.
Costa suffered a muscle injury in the adductors of his left thigh, according to a statement on the club's website.
Atletico Madrid were already preparing to open the season without the 30-year-old, who was issued an eight-match ban in April.
Costa insulted match official Gil Manzano during Atletico's 2-0 loss to Barcelona. He also allegedly grabbed the referee by the arm during the heated exchange.
One match remains on his suspension after missing Atletico Madrid's final seven matches of the 2018-19 campaign.
Altetico Madrid kick off the new season against Getafe on Sunday.