Ben is going to miss next month's 100 because of his workload.
The Northern Superchargers were to have played in the tournament.
He will feature in the one-day international series that starts next week, despite missing the Twenty20 series.
During England's tour of the West Indies in March, the player had a knee problem.
The Durham all-rounder missed the start of the Championship season as he tried to manage his injury.
He missed the T20 World Cup in order to rest his finger and take a break from cricket.
In his first two months as England's Test captain, he led the team to a 2-0 series win over New Zealand and a 2-2 series draw against India.
Matthew Potts has been called up to the England limited-overs squad for the first time after impressing in all four of England's Tests this summer.
The England and Wales Cricket Board allowed Adil to make the pilgrimage to Mecca after he missed the recent series against India.
Bairstow was left out of the India series but is back in the T20 squad.
The first day-night one-day international between England and South Africa will be held on Tuesday.
The England squad for the upcoming one-day internationals are as follows.
England will play a T20 series against India.
The analysis is by Stephan Shemilt.
It's significant that the biggest name in English cricket won't take part in The Hundred, even if it's only for a few games.
It shows how serious England are about protecting him and how much they care about Test cricket.
One of the few three-format players left in the England set-up has a lot on his plate.
The T20 World Cup and Test tour of Pakistan precede the Christmas season.
It's a blow for the competition, but it's the right thing to do.
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