Mbappe, signed from Paris Saint-Germain this year, has been in fine form this season, scoring seven goals for Real in nine matches across all competitions.
The forward was substituted in the 80th minute of the 3-2 home win over Deportivo Alaves in LaLiga on Tuesday and gestured to his thigh while leaving the pitch.
"Following tests carried out today by Real Madrid's Medical Services on our player Kylian Mbappe, he has been diagnosed with an injury to the biceps femoris in his left leg," Real said in a statement. "His progress will be monitored."
Spanish media reported that Mbappe will be ruled out of Sunday's match against Atletico.
Real are second in the LaLiga standings on 17 points, one behind Barcelona who have a game in hand and host second-bottom Getafe later on Wednesday.