The Italian international will not be fit in time for the Premier League contest on Sunday.
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The 22-year-old had to come off during a 1-0 Champions League win over Shakhtar Donetsk.
Calafiori underwent scans on Wednesday, per The Mirror, which revealed a slight injury.
He will be absent for around three weeks, as there is small damage to his medial collateral ligament in his right knee.
However, he does not have a serious knee injury, which would have been a fear for the club.