The 20-year-old suffered the injury during the early stages of the 3-1 England B win over Albania at Turf Moor on Friday.
Lennon was sent for a scan and the results confirmed he will miss the Wembley meeting with Brazil on Friday and the trip to Tallinn on Wednesday week.
Lennon's withdrawal from the England squad makes it even more likely that recalled former England skipper David Beckham will play against both teams.
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