But in good news for Atletico, midfielder Arda Turan could still prove his fitness ahead of the Champions League decider against Real Madrid on May 24.
Costa and Turan both limped off in the opening 25 minutes of Atletico's title-clinching 1-1 draw at Barcelona in La Liga on Saturday, with the former spotted in tears on the bench following a reoccurrence of a hamstring injury.
After the match, Atletico president Enrique Cerezo claimed Costa will miss the Champions League final in Lisbon, while Turan is expected to return to training in a couple of days after aggravating a hip injury versus Barcelona.
Spanish newspaper AS quoted Cerezo as saying Costa will be out for 'at least two weeks', which also casts doubt on the striker's hopes of being fit for the World Cup.
Spain coach Vicente del Bosque must confirm his final 23-man squad by June 2.
Costa pulled up in the opening quarter-hour at the Camp Nou, after looking to surge forward to contribute to an Atleti counter-attack and had to be brought off in the 16th minute.
Turan came off seven minutes later following a collision with Barcelona midfielder Cesc Fabregas but reports throughout the Spanish media indicate he will only be sidelined for up to three days, which should give him a chance to make Diego Simeone's squad for the trip to Lisbon.
Costa has scored 36 goals in all competitions for Atleti this season, while Turan has hit the back of the net nine times.
Turan has six assists, while Costa has created seven goals for his Atleti teammates.
