American Kevin Mitchell is Casey's replacement in the 144-man field at TPC Sawgrass, where the tournament gets underway on Thursday.
World number 12 Casey has been in excellent form this year.
The 40-year-old won the Valspar Championship in Florida in March, holding off Tiger Woods and Masters champion Patrick Reed by one stroke.
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Casey also threatened the course record of 63 in the final round at the U.S. Masters in April, before finishing with two straight bogeys for a 65.
He tied for fifth last Sunday at the Wells Fargo Championship in Charlotte.
(Reporting by Andrew Both; Editing by Toby Davis)
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