The England and Wales Cricket Board has confirmed that both players have suffered a recurrence of their injury problems.
Anderson has pulled out of the Test squad due to a shoulder issue, which he picked up in the summer, and the ECB has claimed that he "requires more time to ensure optimal healing of a stress fracture".
Wood has been troubled by an ankle injury since last winter, and despite undergoing two operations, he has not been declared fit enough to travel with the England team to Bangladesh.
The seam bowler will miss three one-day internationals, as well as two Tests, while he recovers.
The ECB added: "Both players will be reviewed by the ECB's medical team on a regular basis and further updates will be provided on their progress in due course."