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Foad, from Southampton, had the screws fixed in his spine after London 2012.
The 28-year-old, who won European Championship men's pair gold with Matt Langridge in May, will have surgery on Monday to replace them.
"As much as I want to try and push through it and hope everything will be ok, it won't," he wrote on his blog.
"I'm sad to say my 'Road to Rio' has come to an end. I'll never make it in time."
Foad had surgery to fit flexible metal rods into his spine after he won bronze in the men's eight at London 2012.
After suffering three flare ups over the past six months, he had an exploratory operation and it was discovered that four of the screws are loose, with one compressing nerves in his spine. Consequently, the metal needs to be removed and replaced.
"The thought of this year being a write-off and not being able to at least try and complete my goal of competing at the Olympics again is heartbreaking," Foad added.
"As for the future, I'm not really sure what the plan is now. I had planned to retire after Rio, but the whole situation has thrown a spanner in the works.
"At the minute, it doesn't feel satisfying walking away from it like this, but I'll have to see how things go after surgery."
Olympic bronze medallist James Foad will miss this summer's Rio Games, and could retire from rowing after metal screws in his back came loose.