The Spain international had to be withdrawn shortly after half-time of Atletis defeat to Sporting on Thursday night, though they still progressed to the next round thanks to their first-leg victory.
Next up in the competition, Diego Simeones men will take on Arsenal after the two sides were drawn against each other in Fridays draw in Nyon, Switzerland.
And now Atletico have confirmed that he has injured his left hamstring, which typically takes at least a fortnight to recover from – which would rule him out of the first leg at the Emirates.
A statement from the Spanish club confirmed: Our striker suffered an injury in our UEFA Europa League quarter-final match against Sporting CP.
Diego Costa had to be taken off in the 52nd minute on Thursdays match against Sporting CP.
After undergoing medical exams this Friday, April 13, he has been diagnosed with a hamstring injury to his left leg.
Atletico have not provided a return date, though he is unlikely to have recovered for the trip to north London on Thursday, April 26.
Costa had taken part in the last 10 La Liga matches for Atletico, and started both Europa League quarter-final legs, and appeared to be getting back to peak fitness after six months out of the game while he waited to move to Madrid from Chelsea.
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