The 24-year-old will have an operation next week and it is hoped he will be back for the start of the 2018 season.
New Zealander Quinn joined Essex in December 2015 but is not an overseas player as he has a UK passport.
Quinn has taken 101 first-class wickets at an average of 28.40 and registered career-best figures of 7-76 against Gloucestershire last season.
Essex are top of Division One in the County Championship with a 29-point lead over Lancashire in second.
Essex fast bowler Matt Quinn has been ruled out for the rest of the summer because of a persistent back problem.