The full-back has returned to Southampton for further tests on the problem, a decision that has been described by the Football Association as a precautionary measure.
Bertrand will miss the matches with Netherlands in Amsterdam on Friday and the visit of Italy to Wembley next Tuesday.
Danny Rose and Ashley Young are the players most likely to start on the left of the England defence in Bertrand's absence.
The 28-year-old has been denied the opportunity to earn a 20th cap for his country as a result of picking up an untimely knock.
He is also missing out on the chance to reinforce his squad standing in the eyes of Gareth Southgate, as the England coach begins to piece together his plans for the 2018 World Cup.