The bonus was offered to any Japan-based horse in an attempt to attract them to the race.
A veterinarian's examination revealed the continued problem, officials said.
"He had an increased pulse in his foot... Just wasn't sound," NYRA equine medical director Scott Palmer told reporters.
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"In a week maybe he could be ready, but we ran out of time."
Epicharis had been treated for lameness on Wednesday and had not worked out for three days.
The withdrawal left the Belmont Stakes, the third leg in the U.S. Triple Crown, with only 11 horses in the field.
The race was already missing Kentucky Derby winner Always Dreaming and Preakness champion Cloud Computing.
(Reporting by Gene Cherry in Raleigh, North Carolina, editing by Pritha Sarkar)
