The left-armer missed England's resounding victory in the first match of the series on Tuesday and has not recovered in time from an injury sustained during the final Test against India at the Oval almost a fortnight ago.
The selectors have not named a replacement for Friday's day-nighter in Bristol and Monday's clash at Edgbaston. Sidebottom will be examined again on Monday before a decision is made to call in a replacement.
The ECB also confirmed that fast bowler Stephen Harmison would miss the remainder of the domestic season because of a torn muscle in his back.
Harmison, who missed all three Tests against India, will be out for six to eight weeks.
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