"Really sad to withdraw," the Englishman said on Twitter.
"I've been up all night with terrible sickness. Not ideal but felt it worse ... to take spot from reserve if I wasn't able to finish."
Willett still has three weeks to hone his game for the year's first major championship.
He has played only five tournaments worldwide this year, with one finish inside the top 50 -- a tie for fifth at the Maybank Championship in Malaysia.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Larry Fine)
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