The 26-year-old Australian had his left thumb put in a cast after last month's Masters in an effort to speed up the ligament healing process.
"Day suffered a slight setback while playing the Masters and the thumb has been a bit slow to heal," Day's agent said in a statement. "He is still a few weeks away from resuming normal golf activities."
The May 8-11 Players Championship at the TPC Sawgrass in Ponte Vedra, Florida, is the PGA Tour's flagship event.
(Reporting by Andrew Both in Charlotte, North Carolina; Editing by Frank Pingue)
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