The Turkey international pulled out of training on Wednesday after experiencing discomfort when practicing shots on goal.
And tests have now confirmed that the 27-year-old has suffered a "grade II myosfascial muscle injury between the semitendinosus and biceps femoris at the back of the right thigh."
It remains to be whether - or for how long - Turan will be on the sidelines, although the news will come as a disappointment to Atleti as they prepare for the defence of the Liga title they won for the first time since 1996 last season.
Turan is suspended for both legs of Atleti's Supercopa de Espana tie with city rivals Real Madrid, although coach Diego Simeone will hope he will be fit to return in time for their La Liga opener at neighbours Rayo Vallecano a week on Monday.
Simeone's men take on Cadiz in their final pre-season friendly on Friday before travelling to the Santiago Bernabeu for the first leg with Real next Tuesday, with the return game taking place at Estadio Vicente Calderon three days later.
