According to reports in Spain, the Atletico Madrid striker underwent tests at the Clinica Cemtro de Madrid on Monday morning after lasting less than 10 minutes of Saturday's Champions League final against Real Madrid.
After the tests, doctor Pedro Guillen told Cadena Cope radio that the 25-year-old had suffered a grade one tear in the femoral biceps of his right leg and would need to rest for 15 days before the injury is re-evaluated.
"Diego Costa is still carrying the injury, a micro-tear in the hamstring," Guillen, who examined the player, was quoted as saying by the Spanish press.
That would rule Costa out of Spain's pre-World Cup friendlies against Bolivia (May 30) and El Salvador (June 7) and has cast further doubts over the striker's chances of going to Brazil.
Although Spain's first Group B match is not until June 13, coach Vicente del Bosque said on Sunday that he would like all of his players to be fit by the time he has to send his final 23-man squad list to FIFA on June 2.
"We don't know the physical state of everyone and until June 2 we are not obliged to give the list to FIFA," Del Bosque said.
"We would like that on the second everybody who has been called up can train. The World Cup starts against Holland and we want everyone to be ready to go."
Whether Del Bosque will be willing to take a risk on Costa remains to be seen.
The Spain coach has plenty of attacking options to choose from, but Costa has undoubtedly had the best season of any of them.
The Brazil-born forward, who committed his allegiance to Spain last year and made his debut for the reigning world and European champions this March, scored 36 goals in all competitions to help Atletico win their first Primera Division title since 1996 and also reach the Champions League final.
Costa has been struggling with injury for the last few weeks of the season, though, and he limped out of Atletico's final league game against Barcelona the weekend before last with a hamstring problem.
Against expectations, Costa managed to make Atletico's starting line-up for this weekend's Champions League final, but was able to play just nine minutes of the 4-1 defeat before having to be replaced.