Champions Leicester, who guaranteed their Premier League survival last week with a 3-0 victory over Watford, face Manchester City on Saturday when they could also be without central defender Robert Huth who has a foot injury.
"We need to give him (Drinkwater) time to recover from this. I can't see him playing this season. It is weeks rather than months," Shakespeare told reporters.
Leicester are also missing defender Wes Morgan due to injury.
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(Reporting by Martyn Herman, editing by Ed Osmond)
