The 24-year-old, who joined Chelsea for a club record £60m from Real Madrid, is the club’s top scorer with seven goals.
Spanish team doctors diagnosed the grade two myofascial injury and he will miss this week’s World Cup qualifiers against Albania and Israel.
Muscle injuries such as this can take four to eight weeks to recover from.
Spain are top of group G, three points clear of Italy, with two games remaining.
Chelsea next play Crystal Palace on 14 October, before games against Roma, Watford and Everton.
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