The eight-year-old was 6-1 joint second favourite -- behind Might Bite at 3-1 -- to become the first horse to retain the trophy since Best Mate achieved the feat in 2003.
Harrington said the horse had suffered a hairline fracture, eight days before the March 16 race, which was "a massive blow" to her stables and the Potts family who own the horse.
"It's most unfortunate," she told the Racing Post. "We were very much looking forward to him going back to Cheltenham to try and win the race for the second time."
It is the third year in a row the champion has missed the race after Coneygree and Don Cossack did not defend their crown.
"He (Sizing John) cantered as normal this morning at Commonstown and during routine checks this afternoon was found to be sore behind," Harrington said in her Unibet blog.
The 2014 winner Lord Windermere was the last horse to contest the following year's Gold Cup.
The Cheltenham Festival starts on Tuesday.
(Writing by Ken Ferris; Editing by Ed Osmond)
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