Reed, 38, won gold in the coxless four for Britain at Beijing 2008 and London 2012 before switching to the men’s eight in Rio and adding a third Olympic crown.
He admitted there was a "very small chance" he would make a full recovery, with doctors unsure what caused his stroke.
A spinal stroke occurs when the blood supply to the spinal cord is disrupted.
Team GB's double Olympic champion Glover wins gold on rowing comeback
Scott Durant, Tom Ransley, Andrew Hodge, Matt Gotrel, Pete Reed, Paul Bennett, Matt Langridge, William Satch and Phelan Hill
Image credit: Getty Images
"There is a very small chance I will make no recovery and a very small chance I will make a full recovery," Reed wrote on Instagram.
"Much more likely it will be somewhere in between. To what extent depends on the extent of the damage (which we can’t see) and how well I rehab.
"All the other news is great. My arms are still strong and my brain is still as average as it ever was."
Reed also won five gold medals and three silver medals at the World Championships.
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