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.
(Reporting by Martyn Herman, editing by Ed Osmond)
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