The Spain international has struggled with a hamstring problems throughout the campaign, but his latest setback will be a blow for Atleti with the league and UEFA Champions League coming to their conclusions this month.
Costa has scored 36 goals in 50 appearances for Diego Simeone's men in all competitions this season, but he did not train with the squad on Friday ahead of Sunday's clash with Malaga.
"Diego Costa has gone through some imaging tests that determine muscle injury grade one femoral biceps muscle in the back of his right thigh," the club confirmed on Friday.
"These tests, performed in the Clinica Fremap de Majadahonda have determined that there is no breakage.
"The injury is awaiting developments.
"The forward did not train with his teammates in the morning session on Friday."
Atleti are currently three points clear at the top of La Liga with two matches left to play.
The news of Costa's injury will also come as a concern to Spain coach Vicente Del Bosque who could include Costa in his squad for the FIFA World Cup in Brazil.
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