The 23-year-old Hicks was diagnosed in high school as having Type 1 diabetes.
Hicks, who routinely tops 100 mph, is recovering from Tommy John surgery on June 26, 2019. The right-hander's availability for this season was uncertain.
Hicks had been taking part in workouts at Busch Stadium, leading up to the Cardinals' opener on July 24 at home against Pittsburgh.
"We respect and understand Jordan's decision to opt out this season," Cardinals President of Baseball Operations John Mozeliak said. "We wish him well as he continues his recovery from elbow surgery, and we look forward to seeing Jordan back on the mound for the 2021 season."
Dodgers pitcher David Price, Giants catcher Buster Posey and Washington infielder Ryan Zimmerman are among about a dozen players who have opted out this year.
Hicks was 2-2 with 14 saves and a 3.14 ERA last season before he injured his elbow. He has hit 105 mph with his fastball.
Hicks was due $214,370 as a prorated share of his $578,800 salary. He gets paid if the pre-existing health concern has been determined to make him a high-risk individual.
Ryan Helsley and Giovanny Gallegos are expected to handle the late innings out of the Cardinals' bullpen.