Cook's captaincy has been frequently questioned since an Ashes whitewash at the hands of Australia.
Subsequent ODI series defeats to Australia, Sri Lanka and India have led many to call for Cook to step away from the shorter format.
Even a 3-1 Test triumph over India saw the 29-year-old overcome a torrent of negativity, though public backing at the Ageas Bowl - where Cook hit 95 and an unbeaten 70 in an impressive win - showed his talents in the five-day game remain appreciated.
However, recent ODIs have been disastrous for the England skipper, who has passed 50 just once in 14 outings.
An ECB release revealed he was the only contracted player to be withdrawn from the final two rounds of the County Championship - though fellow batsman Ian Bell will only be permitted to feature in Warwickshire's Royal London One-Day Cup final if he recovers from a fractured toe.
Cook is likely to return to action when England begin a seven-game ODI series in Sri Lanka on November 26.
The remainder of England's batsmen are free to represent their counties, though the bowlers have seen their availability limited.
"England management have requested that seam bowlers are unavailable for the final week of the season with a view to giving them a six-week break from bowling before building up to the tour to Sri Lanka," the ECB confirmed.