The Spain international was susbtituted early on during his side's 1-1 draw with Barcelona on Saturday and was reduced to tears whilst receiving treatment on the sidelines.
The club have now confirmed that he has suffered a grade one hamstring injury, throwing his chances of playing against Real Madrid into serious doubt, while also raising concerns over his availability for the World Cup starting next month.
"Diego Costa has suffered a grade one muscular injury to the femoral bicep of the back of his right leg," the club said on Twitter before adding that they are waiting for definitive news on the length of time needed for the striker's recovery.
Costa - who will join Chelsea in a £35 million deal this summer - has scored 36 goals in all competitions as Atletico soared to an historic Primera Division a title as well as a place in the Champions League final.
The Brazil-born star was struggling with a hamstring problem prior to Saturday's decider at Camp Nou but coach Diego Simeone had insisted that he was ready to play following midweek training.