Defending champion Pieters, 24, was stung during a challenge round earlier in the week.
"The very unfortunate worst case scenario just happened.... One bee sting on Monday during the golf challenge against @joostluitengolfer led to a major allergic reaction with flu symptoms, and forced me to pull out of my favourite tournament of the year," the Belgian said on his Instagram account.
"Very sorry to all the fans that are on their way to support me and to the organisation. I owe it to you guys to defend my title next year."
Pieters, one of the longest hitters in the game, will make his Ryder Cup debut for Europe against the U.S. at Hazeltine, Minnesota at the end of the month.
He is one of six rookies in the 12-man European team who will be defending the title.
(Reporting by Martyn Herman; editing by Sudipto Ganguly)
