The 29-year-old is recovering from a chest infection and slight hamstring issue and has withdrawn from the March 17-20 event in Portland, Oregon.
"Defending the Olympic title is obviously Greg’s main focus for 2016, so he has sensibly decided not to take any risks and to end his indoor season here," British Athletics Performance Director Neil Black said.
"This will allow him the opportunity to concentrate on being in the best shape possible going into the outdoor season and ultimately Rio."
(Editing by Ossian Shine and Janet Lawrence)
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