The Brazil-born Spain international has spearheaded his side's charge to the top of the Primera Division with 27 goals in 34 appearances.
He was unable to prevent a 2-0 loss to Levante last week and is unlikely to participate against Malaga on Sunday, though he should be fit to face Barcelona the following week.
"Diego Costa underwent tests to determine the extent of the grade one thigh injury muscle on his right leg," a club statement reads.
"These tests have confirmed that there is no tear. The forward did not train with his team-mates in the morning session on Friday."
Costa suffered a similar injury against Barcelona during the first leg of their Champions League tie.
Atleti face Malaga on home soil on Sunday before travelling to Camp Nou for a mouth-watering clash on the final day of the season.