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.
Essex will not replace injured New Zealand international fast bowler Adam Milne in their T20 Blast squad.