The 31-year-old former Valencia CF player picked up the injury while on international duty earlier this month. He has appeared once in Serie A and once in the UEFA Champions League this season, and will miss the remainder of the group stage in the latter competition.
Kily, who joined Inter in 2003, missed the first half of last season with a serious knee injury but by April was a regular, appearing 14 times as Inter finished third and won the Coppa Italia. The club have six points from three games in this season's UEFA Champions League.
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