The Sussex all-rounder had the operation to correct a nerve issue which has been affecting him for some time and the club's medical team say he will be out of action for 6-10 weeks.
It means he will almost certainly miss the county’s red-ball campaign when it starts on August 1, although there is a chance he could play some part in the Vitality Blast in September.
Jordan, 31, has been managing the injury since it first flared up five years ago without many issues but last year it started to cause pain in his right elbow and Sussex decided that he needed an operation to decompress the nerve. Successful surgery took place on Monday.
Meanwhile, virtually all the Sussex players are now back in training at Hove and preparing for the start of the Bob Willis Trophy red-ball competition on August 1.
Fast bowlers Stuart Meaker, Mitch Claydon, George Garton, Will Sheffield and Aaron Thomason returned last week, joining up with Phil Salt and Laurie Evans who have been training together since last month. Salt and Evans were among 24 players named on Thursday in England’s one-day squad for the series against Ireland at the end of the month.
The only absentees are Luke Wright and Tymal Mills, who will start training in time for the Vitality Blast competition in September.