The 34-year-old will miss Lancashire's return fixture against Yorkshire starting June 2 as he will be assessed by England's medical team to understand the extend of the injury.
Anderson, who missed four of England's last 10 tests with a shoulder injury, could still feature in three county matches in June to prove his fitness ahead of the international season.
England host South Africa in first of four tests starting on July 6 at Lord's before welcoming West Indies in a three-match series to wrap up the test summer in August and September.
(Reporting by Hardik Vyas in Bengaluru; Editing by Keith Weir)
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