The 24-year-old was scheduled to play seven group games, but will now undergo elbow surgery without making an appearance in the competition.
The club will instead give their young players a chance to feature.
"We are looking forward to seeing how the young players go when given an opportunity," head coach Chris Silverwood said.
"As a club we are renowned for investing in youth and we will continue to do so to improve their experiences over the remaining matches of the campaign. Giving them opportunities now will only help them in the future."
Meanwhile, bowling coach Donovan Miller has left the club for Caribbean Premier League side Jamaica Tallawahs.
Miller played club cricket in the Middlesex, Essex and Hertfordshire leagues from 2000-2012, while completing his coaching qualifications.
"I am delighted to be joining the Tallawahs. I have put a lot of effort in over the years to ensure I keep getting better as a coach," he said.
Former England one-day wicketkeeper Paul Nixon is Tallawahs head coach.

Holyrood Park Distillery is looking to raise £5.5m from investors for a new distillery and visitor centre.
The funds will be used to renovate a former engine shed in St Leonard's Lane and buy and install equipment.
The cash will also be used to help cover early start-up and production costs.
Fundraising will be led by accountants and business advisers Johnston Carmichael.
Plans for the distillery were approved last year by the City of Edinburgh Council.
It is a joint development by David Robertson, former master distiller for The Macallan, and Rob and Kelly Carpenter, founders of the Canadian branch of The Scotch Malt Whisky Society.
Mr Carpenter said: "We are confident that by placing a working distillery in the heart of Edinburgh's capital, with the visitor numbers and cash flow that is expected to provide, we are creating something that is quite different from the typical distillery start-up."
The Holyrood Distillery will be Edinburgh's first single malt whisky distillery since Glen Sciennes closed in the 1920s.
There are also plans to produce gins, liqueurs and other spirits.
Distilling of Holyrood whisky is due to begin in late 2018, with bottles hitting the shelves as early as 2021, according to the company.
Essex will not replace injured New Zealand international fast bowler Adam Milne in their T20 Blast squad.
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The company behind plans to bring single malt whisky distilling back to Edinburgh after a 90-year absence have launched a major fundraising drive.